singular continuous spectrum for palindromic schrodinger operators we give new examples of discrete schrodinger operators with potentials taking finitely many values that have purely singular continuous spectrum if the hullx of the potential is strictly ergodic then the existence of just one potentialx inx for which the operator has no eigenvalues implies that there is a generic set inx for which the operator has purely singular continuous spectrum a sufficient condition for the existence of such anx is that there is az x that contains arbitrarily long palindromes thus we can define a large class of primitive substitutions for which the operators are purely singularly continuous for a generic subset inx the class includes well known substitutions like fibonacci thue morse period doubling binary non pisot and ternary non pisot we also show that the operator has no absolutely continuous spectrum for allx x ifx derives from a primitive substitution for potentials defined by circle maps x n 1 j 0 n we show that the operator has purely singular continuous spectrum for a generic subset inx for all irrational and every half open intervalj

gleason s theorem for rectangular jbw triples a jbw triple b is said to be rectangular if there exists a w algebra a and a pair p q of centrally equivalent elements of the complete orthomodular lattice of projections in a such that b is isomorphic to the jbw triple paq any weak closed injective operator space provides an example of a rectangular jbw triple the principal order ideal of the complete lattice of centrally equivalent pairs of projections in a w algebra a generated by p q forms a complete lattice that is order isomorphic to the complete lattice of weak closed inner ideals in b and to the complete lattice of structural projections on b although not itself in general orthomodular possesses a complementation that allows for definitions of orthogonality centre and central orthogonality to be given a less familiar notion in lattice theory that is well known in the theory of jordan algebras and jordan triple systems is that of rigid collinearity of a pair e2 f2 and e2 f2 of elements of this is defined and characterized in terms of properties of a w algebra a is sometimes thought of as providing a model for a statistical physical system in this case b or equivalently paq may be thought of as providing a model for a fixed sub system of that represented by a therefore may be considered to represent the set consisting of a particular kind of sub system of that represented by paq central orthogonality and rigid collinearity of pairs of elements of may be regarded as representing two different types of disjointness the former classical disjointness and the latter decoherence of the two sub systems it is therefore natural to consider bounded measures m on that are additive on centrally orthogonal and rigidly collinear pairs of elements using results of j d m wright it is shown that provided that neither of the two hereditary sub w algebras pap and qaq of a has a weak closed ideal of type i2 such measures are precisely those that are the restrictions of bounded sesquilinear functionals m on pap qaq with the property that the action of the centroid z b of b commutes with the adjoint operation when b is a complex hilbert space of dimension greater than two this result reduces to gleason s theorem

algebras of quotients of graded lie algebras abstract in this paper we explore graded algebras of quotients of lie algebras with special emphasis on the 3 graded case and answer some natural questions concerning its relation to maximal jordan systems of quotients

strong primeness of hermitian jordan systems this paper establishes the strong primeness of all jordan systemsjof hermitian type trapped between ample hermitian elements of a prime associative systemrand its martindale system of symmetric quotientsq r h0 r j h q r this completes the converse of zelmanov s classification of strongly prime jordan systems providing if as well as only if classifications of strongly prime and primitive jordan systems

chaotic scattering theory of transport and reaction rate coefficients the chaotic scattering theory is here extended to obtain escape rate expressions for the transport coefficients appropriate for a simple classical fluid or for a chemically reacting system this theory allows various transport coefficients such as the coefficients of viscosity thermal conductivity etc to be expressed in terms of the positive lyapunov exponents and kolmogorov sinai entropy of a set of phase space trajectories that take place on an appropriate fractal repeller this work generalizes the previous results of gaspard and nicolis for the coefficient of diffusion of a particle moving in a fixed array of scatterers

fractal fractal dimensions of deterministic transport coefficients if a point particle moves chaotically through a periodic array of scatterers the associated transport coefficients are typically irregular functions under variation of control parameters for a piecewise linear two parameter map we analyse the structure of the associated irregular diffusion coefficient and current by numerically computing dimensions from box counting and from the autocorrelation function of these graphs we find that both dimensions are fractal for large parameter intervals and that both quantities are themselves fractal functions if computed locally on a uniform grid of small but finite subintervals we furthermore show that there is a simple functional relationship between the structure of fractal fractal dimensions and the difference quotient defined on these subintervals

an alternative daugavet property abstract we introduce a strictly weaker version of the daugavet property as follows a banach space x has this alternative daugavet property adp in short if the norm identity ade max 1 id t 1 t holds for all rank one operators t x x in such a case all weakly compact operators on x also satisfy ade we give some geometric characterizations of the alternative daugavet property in terms of the space and its successive duals we prove that the adp is stable for c0 l1 and l sums and characterize when some vector valued function spaces have the property finally we show that a c algebra or the predual of a von neumann algebra has the adp if and only if its atomic projection respectively the atomic projection of the algebra are central we also establish some geometric properties of jb triples and characterize jb triples possessing the adp and the daugavet property

linear invariance of locally biholomorphic mappings in the unit ball of a jb triple abstract we study the notion of linear invariance on the unit ball of a j b triple x and we obtain some connection between the norm order of a linear invariant family and the starlikeness of order 1 2 also we give some result concerning the radius of univalence of some linear invariant families finally if the dimension of x is finite and if the norm order of a linear invariant family is finite then we prove the normality of the linear invariant family and we also obtain upper bounds on the distortion and the growth of mappings in a linear invariant family with specified norm order in particular our results are valid for the classical cartan domains and the unit polydisc

the central hull and central kernel in jbw triples abstract the complete lattice i a of weak closed inner ideals in a jbw triple a has as its centre the complete boolean algebra z i a of weak closed ideals in a the annihilator l of the subset l of a consists of elements b of a for which l b a is equal to zero and the kernel ker l of l consists of those elements b in a for which l b l is equal to zero for each element j of i a j also lies in i a and a enjoys the generalized peirce decomposition a j m j j 1 where j 1 is the intersection of the kernels of j and j to investigate the properties of the weak closed subspace j 1 of a which is not in general a subtriple the notions of the central hull c l and central kernel k l of a subspace l are introduced these are respectively the smallest element of z i a containing l and the largest element of z i a contained in l for any element j of i a the relationships that exist between the central hull and central kernel of j and j are examined and it is shown that j 1 j is the weak closed ideal k j that j 1 j is the weak closed ideal k j and when j is a peirce inner ideal that j 1 is the weak closed ideal k j m k j

the denjoy wolff theorem in the open unit ball of a strictly convex banach space letxbe a complex strictly convex banach space with an open unit ballb for each compact holomorphic and fixed point free mappingf b bthere exists bsuch that the sequence fn of iterates offconverges locally uniformly onbto the constant map taking the value

orthogonality preservers in c algebras jb algebras and jb triples abstract we study orthogonality preserving operators between c algebras jb algebras and jb triples let t a e be an orthogonality preserving bounded linear operator from a c algebra to a jb triple satisfying that t 1 d is a von neumann regular element then t a e 2 r d every element in t a and d operator commute in the jb algebra e 2 r d and there exists a triple homomorphism s a e 2 r d such that t l d r d s where r d denotes the range tripotent of d in e an analogous result for a being a jb algebra is also obtained when t a b is an operator between two c algebras we show that denoting h t 1 then t orthogonality preserving if and only if there exists a triple homomorphism s a b satisfying h s z s z h h s z s z h and t z l h r h s z 1 2 h r h s z s z r h h this allows us to prove that a bounded linear operator between two c algebras is orthogonality preserving if and only if it preserves zero triple products

the lattice of weak closed inner ideals in a w algebra the family of centrally equivalent pairs of projections in a w algebra a forms a complete lattice that is order isomorphic to the complete lattice of weak closed inner ideals in a and to the complete lattice of structural projections on a furthermore the set of symmetric elements of is order isomorphic to the complete orthomodular lattice of projections in a although not itself in general orthomodular possesses a complementation that allows for definitions of orthogonality centre and central orthogonality to be given a less familiar notion in lattice theory that is well known in the theory of jordan algebras and jordan triple systems is that of rigid collinearity of a pair e1 f1 and e2 f2 of elements of this is defined and characterized in terms of properties of

the fractality of the relaxation modes in reaction diffusion systems abstract in chaotic reaction diffusion systems with two degrees of freedom the modes governing the exponential relaxation to the thermodynamic equilibrium present a fractal structure which can be characterized by a hausdorff dimension for long wavelength modes this dimension is related to the lyapunov exponent and to a reactive diffusion coefficient this relationship is tested numerically on a reactive multibaker model and on a two dimensional periodic reactive lorentz gas the agreement with the theory is excellent

dunford pettis properties hilbert spaces and projective tensor products we study complete continuity properties of operators onto 2 and prove several results in the dunford pettis theory of jb triples and their projective tensor products culminating in characterisations of the alternative dunford pettis property for e f where e and f are jb triples

images of contractive projections on operator algebras it is shown that if p is a weak continuous contractive projection on a jbw triple m then p m is of type i or semifinite respectively if m is of the corresponding type we also show that p m has no infinite spin part if m is a type i von neumann algebra

chaotic scattering and diffusion in the lorentz gas a chaotic scattering theory of diffusion in the lorentz gas is presented the scattering process is considered on disk scatterers of increasing sizes in this way chaotic and fractal properties of the scattering process are related to diffusion a formula is obtained that gives the diffusion coefficient in terms of the lyapunov exponent and the hausdorff codimension of the fractal repeller of orbits trapped in the scatterer numerical results are presented that support our theoretical results

tits kantor koecher lie algebras of jb triples abstract we characterise the tits kantor koecher lie algebra of a jb triple which can be infinite dimensional in particular we show that a complex lie algebra is the tits kantor koecher lie algebra of a jb triple if and only if it has a real form which is isomorphic to the reduced lie algebra of a bounded symmetric domain matrix representations of these lie algebras are also presented

weakly compact orthogonality preservers on c algebras we establish a complete description of weakly compact orthogonality preserving operators from a c algebra a or a jb algebra to a jb triple e we prove that any such operator is the sum of a series of mutually orthogonal triple homomorphisms from a to a certain peirce 2 subspace of e multiplied by a mutually orthogonal norm null sequence in e which enjoy certain operator commutativity relations

deterministic models of the simplest chemical reactions we present a general mathematical framework for constructing deterministic models of simple chemical reactions in such a model an underlying dynamical system drives a process in which a particle undergoes a reaction changes color when it enters a certain subset the catalytic site of the phase space and possibly some other conditions are satisfied the framework we suggest allows us to define the entropy of reaction precisely and does not rely as was the case in previous studies on a stochastic mechanism to generate additional entropy thus our approach provides a natural setting in which to derive macroscopic chemical reaction laws from microscopic deterministic dynamics without invoking any random mechanisms

automatic continuity of derivations on c algebras and jb triples abstract we introduce the notion of banach jordan triple modules and determine the precise conditions under which every derivation from a jb triple e into a banach jordan triple e module is continuous in particular every derivation from a real or complex jb triple into its dual space is automatically continuous motivating the study which we have carried out elsewhere of weakly amenable jb triples specializing to c algebras leads to a unified treatment of derivations and jordan derivations into modules shedding light on a celebrated theorem of barry johnson

on the facial structure of the unit ball in the dual space of a jb triple it is shown that every proper weak closed face of the closed unit ball e 1 in the dual space of a jb triple e coincides with set of all elements in the unit sphere of e attaining their norm at a unique compact tripotent in e in particular every proper weak closed face of the closed unit ball e 1 is weak semi exposed this result provides an affirmative answer to a conjecture posed over 20 years ago

operator space structure of jc triples and tros i we embark upon a systematic investigation of operator space structure of jc triples via a study of the tros ternary rings of operators they generate our approach is to introduce and develop a variety of universal objects including universal tros by which means we are able to describe all possible operator space structures of a jc triple via the concept of reversibility we obtain characterisations of universal tros over a wide range of examples we apply our results to obtain explicit descriptions of operator space structures of cartan factors regardless of dimension

fractals and dynamical chaos in a two dimensional lorentz gas with sinks we consider a two dimensional periodic reactive lorentz gas in which a moving point particle undergoes elastic collisions on fixed hard disks and annihilates on absorbing disks called sinks we present clear evidence of the existence of a fractal repeller in this open system moreover we establish a relation between the reaction rate describing the macroscopic evolution of the system and two characteristic quantities of the microscopic chaos the average lyapunov exponent and the hausdorff codimension of the fractal repeller

projective completions of jordan pairs part i the generalized projective geometry of a lie algebra abstract we prove that the projective completion x x of the jordan pair g 1 g 1 corresponding to a 3 graded lie algebra g g 1 g 0 g 1 can be realized inside the space f of inner 3 filtrations of g in such a way that the remoteness relation on x x corresponds to transversality of flags this realization is used to give geometric proofs of structure results which will be used in part ii of this work in order to define on x and x the structure of a smooth manifold in arbitrary dimension and over general base fields or rings

geometric characterization of tripotents in real and complex jb triples abstract we establish a geometric characterization of tripotents in real and complex jb triples as a consequence we obtain an alternative proof of kaup s banach stone theorem for jb triples

fractal dimension of transport coefficients in a deterministic dynamical system in many low dimensional dynamical systems transport coefficients are very irregular and are perhaps even fractal functions of control parameters to analyse this phenomenon we study a dynamical system defined by a piecewise linear map and investigate the dependence of transport coefficients on the slope of the map we present analytical arguments supported by numerical calculations showing that both the minkowski bouligand and hausdorff fractal dimension of the graphs of these functions is 1 with a logarithmic correction and we find that the exponent controlling this correction is bounded from above by 1 or 2 depending on some detailed properties of the system using numerical techniques we show local self similarity of the graphs the local self similarity scaling transformations turn out to be dependent irregularly on the values of the system control parameters

measures on the lattice of closed inner ideals in a spin triple two elements j and k of the complete lattice i a of weak closed inner ideals in a jbw triple a are said to be centrally orthogonal if there exists a weak closed ideal i in a such that a2 j a2 i and a2 k a0 i and are said to be rigidly collinear when a2 j a1 k and a2 k a1 j where for j equal to 0 1 or 2 aj i aj j and aj k are the components in the generalized peirce decomposition of a relative to the weak closed inner ideals i j and k respectively a measure m on i a is a mapping from i a to c such that if j and k are either centrally orthogonal or rigidly collinear thenmj k mj mk a complex hilbert space a endowed with a conjugation possesses a triple product and norm with respect to which it forms a jbw triple known as a spin triple in this paper the structure of the complete lattice i a of closed inner ideals in a spin triple a and the measures on it are investigated it is shown that if the dimension of a is greater than 5 then there are no non zero measures on i a when the dimension of a is 5 non zero measures exist and up to multiplication by a constant a unique measure exists that is invariant under automorphisms of a when the dimension of a is 4 then a is triple isomorphic to the w algebra of 2 2 complex matrices in this case results of bunce and wright are used to show that there is an uncountable number of measures on i a the situation when the dimension of a is less than 4 is also described

fixed points and invariant domains of holomorphic mappings of the hilbert ball this paper is an extension of the joint work of the present author t sekowski and a stachura 4 there some methods of the theory of nonexpansive mappings were used to prove fixed point theorems for holomorphic self mappings of the unit ball in complex hilbert space earlier results on the existence of fixed points of holomorphic self mappings of domains in banach spaces may be found in works of earle and hamilton 2 hayden and suffridge 6 7 111 and rudin 9 all the results depend strongly on the consequences of the schwartz pick lemma and properties of so called invariant hyperbolic metrics detailed discussion of invariant metrics is contained in the long article by harris 5 and in the recent book by franzoni and vesentini 3 hyperbolic geometry of the unit ball in c is clearly described in a very recent book by rudin lo in spite of the fact that we are dealing with the infinite dimensional case we very often follow the notation terminology and some methods from this book a very interesting discussion of the one dimensional case has been given recently by burckel l invariant ellipsoids which we discuss here have their origin in the old papers by julia s and wolff 2

holomorphic automorphisms of continuous products of balls we study continuous product domains in the space cal c omega e of all continuouse valued functions on omega where omega is a compact hausdorff topological space and e is an arbitrary jb triple and discuss the group of holomorphic automorphisms of domains of that type

iteration of self maps on a product of hilbert balls abstract let d d 1 d p be a product of hilbert balls with coordinate maps j d d j on the closure d for j 1 p let f be a fixed point free self map on d which is nonexpansive in the kobayashi distance and compact for p 2 we describe the horospheres invariant under f and show that there exist a boundary point 1 p of d and a nonempty set j 1 p such that each limit function h of the iterates f n satisfies j j h d for all j j and j h j whenever j h d meets the boundary of d j for a single hilbert ball d 1 either l i m i n f n f 2 n 0 1 or f n converges locally uniformly to a constant map taking value at the boundary of d 1

trace order and a distortion theorem for linearly invariant families on the unit ball of a finite dimensional jb triple abstract we give a distortion theorem for linearly invariant families on the unit ball b of a finite dimensional jb triple x by using the trace order the exponents in the distortion bounds depend on the bergman metric at 0 further we introduce a new definition for the trace order of a linearly invariant family on b based on a jacobian argument we also construct an example of a linearly invariant family on b which has minimum trace order and is not a subset of the normalized convex mappings of b for dim x 2 finally we prove a regularity theorem for linearly invariant families on b all four types of classical cartan domains are the open unit balls of jb triples and the same holds for any finite product of these domains thus the unit balls of jb triples are natural generalizations of the unit disc in c and we have a setting in which a large number of bounded symmetric homogeneous domains may be studied simultaneously

state spaces of jb triples an atomic decomposition is proved for banach spaces which satisfy some affine geometric axioms compatible with notions from the quantum mechanical measuring process this is then applied to yield under appropriate assumptions geometric characterizations up to isometry of the unit ball of the dual space of a jb triple and up to complete isometry of one sided ideals in c algebras

low rank compact operators and tingley s problem abstract let e and b be arbitrary weakly compact jb triples whose unit spheres are denoted by s e and s b respectively we prove that every surjective isometry f s e s b admits an extension to a surjective real linear isometry t e b this is a complete solution to tingley s problem in the setting of weakly compact jb triples among the consequences we show that if k h k denotes the space of compact operators between arbitrary complex hilbert spaces h and k then every surjective isometry f s k h k s k h k admits an extension to a surjective real linear isometry t k h k k h k

quadratic jordan systems of hermitian type abstract in this paper we extend zel manov s classification of linear jordan systems triple systems and pairs of hermitian type to quadratic jordan systems over an arbitrary ring of scalars using associative triple systems of the first kind for what we believe to be a more natural tool to describe special jordan triples we show that an i special prime quadratic jordan triple system the ideals of which remain semiprime with a nonzero hermitian part lies between an ample subspace of hermitian elements in a prime associative triple system and those in its martindale system of symmetric quotients modulo some extra definitions the structure of strongly prime jordan pairs of hermitian type follows almost immediately from the jordan triple result

relatively weakly open sets in closed balls of banach spaces and real jb triples of finite rank we prove that given a real jb triple x there exists a nonempty relatively weakly open subset of the closed unit ball of x with diameter less than 2 if and only if the banach space of x is isomorphic to a hilbert space moreover we give the structure of real jb triples whose banach spaces are isomorphic to hilbert spaces such real jb triples are also characterized in two different purely algebraic ways

the daugavet property of c algebras jb triples and of their isometric preduals a banach space x is said to have the daugavet property if every rank one operator t x x satisfies id t 1 t we give geometric characterizations of this property in the settings of c algebras jb triples and their isometric preduals we also show that in these settings the daugavet property passes to ultrapowers and thus it is equivalent to an stronger property called the uniform daugavet property

classical dynamics on graphs we consider the classical evolution of a particle on a graph by using a time continuous frobenius perron operator that generalizes previous propositions in this way the relaxation rates as well as the chaotic properties can be defined for the time continuous classical dynamics on graphs these properties are given as the zeros of some periodic orbit zeta functions we consider in detail the case of infinite periodic graphs where the particle undergoes a diffusion process the infinite spatial extension is taken into account by fourier transforms that decompose the observables and probability densities into sectors corresponding to different values of the wave number the hydrodynamic modes of diffusion are studied by an eigenvalue problem of a frobenius perron operator corresponding to a given sector the diffusion coefficient is obtained from the hydrodynamic modes of diffusion and has the green kubo form moreover we study finite but large open graphs that converge to the infinite periodic graph when their size goes to infinity the lifetime of the particle on the open graph is shown to correspond to the lifetime of a system that undergoes a diffusion process before it escapes

localization in general one dimensional random systems i jacobi matrices we consider random discrete schrodinger operators in a strip with a potentialv n n a label in and a finite label across the strip andv an ergodic process we prove thath0 v has only point spectrum with probability one under two assumptions 1 theconditional distribution of v n n 0 1 all conditioned on v n 0 1 all has an absolutely continuous component with positive probability 2 for a e e no lyaponov exponent is zero

boundedness of completely additive measures with application to 2 local triple derivations we prove a jordan version of dorofeev s boundedness theorem for completely additive measures and use it to show that every not necessarily linear nor continuous 2 local triple derivation on a continuous jbw triple is a triple derivation 2 local triple derivations are well understood on von neumann algebras jbw triples which are properly defined in section i are intimately related to infinite dimensional holomorphy and include von neumann algebras as special cases in particular continuous jbw triples can be realized as subspaces of continuous von neumann algebras which are stable for the triple product xy z zy x and closed in the weak operator topology

singular continuous spectrum under rank one perturbations and localization for random hamiltonians we consider a selfadjoint operator a and a selfadjoint rank one projection p onto a vector which is cyclic for a in terms of the spectral measure d a we give necessary and sufficient conditions for a p to have empty singular continuous spectrum or to have only point spectrum for a e we apply these results to questions of localization in the one and multi dimensional anderson models

pure point spectrum under 1 parameter perturbations and instability of anderson localization we consider a selfadjoint operator a and a selfadjoint rank one projection p onto a vector which is cyclic fora we study the set of all eigenvalues of the operatora t a tp t that belong to its essential spectrum which does not depend on the parametert we prove that this set is empty for a dense set of values oft then we apply this result or its idea to questions of anderson localization for 1 dimensional schrodinger operators discrete and continuous

hydrodynamic modes as singular eigenstates of the liouvillian dynamics deterministic diffusion hydrodynamic modes of diffusion and the corresponding nonequilibrium steady states are studied as an eigenvalue problem for the liouvillian dynamics of spatially extended suspension flows which are special continuous time dynamical systems including billiards defined on the basis of a mapping the infinite spatial extension is taken into account by spatial fourier transforms which decompose the observables and probability densities into sectors corresponding to the different values of the wave number the frobenius perron operator ruling the time evolution in each wave number sector is reduced to a frobenius perron operator associated with the mapping of the suspension flow in this theory the dispersion relation of diffusion is given as a pollicott ruelle resonance of the frobenius perron operator and the corresponding eigenstates are studied formulas are derived for the diffusion and the burnett coefficients in terms of the mapping of the suspension flow nonequilibrium steady states are constructed on the basis of the eigenstates and are given by mathematical distributions without density functions also referred to as singular measures the nonequilibrium steady states are shown to obey fick s law and to be related to zubarev s local integrals of motion the theory is applied to the regular lorentz gas with a finite horizon generalizations to the nonequilibrium steady states associated with the other transport processes are also obtained

aron berner extensions of triple maps with application to the bidual of jordan banach triple systems abstract by extending the notion of arens regularity of bilinear mappings we say that a bounded trilinear map on the cartesian product of banach spaces is aron berner regular when all its six aron berner extensions to the cartesian product of the bidual spaces coincide we give some results on the aron berner regularity of certain trilinear maps we then focus on the bidual e of a jordan banach triple system e and investigate those conditions under which e is itself a jordan banach triple system under each of the aron berner extensions of the triple product we also compare these six triple products with those arising from certain ultrafilters based on the ultrapower formulation of the principle of local reflexivity in particular we examine the aron berner triple products on the bidual of a jb triple in relation with the so called dineen s theorem some illuminating examples are included and some questions are also left undecided

jordan structures in harmonic functions and fourier algebras on homogeneous spaces we study the jordan structures and geometry of bounded matrix valued harmonic functions on a homogeneous space and their analogue the harmonic functionals in the setting of fourier algebras of homogeneous spaces

the range of a structural projection abstract let a be a jbw triple a linear subspace j of a is called an inner ideal in a provided that the subspace j a j is contained in j a subtriple b in a is said to be complemented if a b ker b where ker b a a b a b 0 a complemented subtriple in a is a weak closed inner ideal a linear projection on a is said to be structural if for all elements a b and c in a formula the range of a structural projection is a complemented subtriple and conversely a complemented subtriple is the range of a unique structural projection we analyze the structure of the weak closed inner ideal generated by two arbitrary tripotents in a jbw triple in terms of the simultaneous peirce spaces of three suitably chosen pairwise compatible tripotents this result is then used to show that every weak closed inner ideal j in a jbw triple a is a complemented subtriple in a and therefore the range of a unique structural projection on a as an application structural projections on w algebras are considered

tits kantor koecher algebras of strongly prime hermitian jordan pairs abstract in this paper we describe the tits kantor koecher algebras of strongly prime hermitian jordan pairs in terms of prime associative pairs and their martindale pairs of symmetric quotients

unit free contractive projection theorems for c jb and jb algebras abstract we prove that if a is a possibly non unital non commutative j b algebra and if a a is a positive contractive linear projection then a endowed with the product x y x y becomes naturally a non commutative j b algebra and moreover the equality a b a b holds for all a b a the appropriate variant of this result with jb algebra instead of non commutative j b algebra is also obtained in the non commutative j b case the requirement of positiveness for can be relaxed to the one that the equality holds in general this relaxing is strict but it is not strict if is bicontractive actually positive bicontractive linear projections on non commutative j b algebras are fully described and a structure theorem for bicontractive linear projections without any extra requirement on non commutative j b w algebras is proved finally bicontractive linear projections on c algebras are studied in detail

a wolff theorem for finite rank bounded symmetric domains abstract we present a wolff theorem for all infinite dimensional bounded symmetric domains of finite rank namely if b is the open unit ball of any finite rank j b triple and f b b is a compact holomorphic map with no fixed point in b we prove convex f invariant subdomains of b of all sizes and at all points exist in the form of simple operator balls c t b for c b and t an invertible linear map these are exact infinite dimensional analogues of the invariant discs in the invariant ellipsoids in the hilbert ball and invariant domains in finite dimensional triples results are new for rank 2 even for classical spaces such as c algebras and j b algebras

distortion of locally biholomorphic bloch mappings on bounded symmetric domains abstract we generalize bonk s distortion theorem on the unit disc in the complex plane to locally biholomorphic mappings on finite dimensional bounded symmetric domains as an application we obtain a lower bound for the bloch constant for various classes of locally biholomorphic bloch mappings

operators with singular continuous spectrum i general operators the baire category theorem implies that the family f of dense sets g in fixed metric space x is a candidate for generic sets since it is closed under countable intersections and if x is perfect has no isolated point then a f has uncountable intersections with any open ball in x

generalised f algebras as predual algebras of jbw triples and characterisations of the fourier algebras on locally compact groups abstract we introduce the notion of a generalised f algebra as a banach algebra a whose banach space dual is a j b w triple with a certain additional condition on a distinguished character of a this generalises the well known notion of f algebras which in turn includes as special cases many important classes of banach algebras on locally compact groups and semigroups our main use of this new notion is to give some axiomatic characterisations of the fourier algebras on locally compact groups strengthening our previous work 37 but we also quickly review some well known results in f algebras that can be extended to the context of generalised f algebras

banach space characterizations of unitaries a survey abstract we survey banach space characterizations of unitary elements of c algebras jb triples and jb algebras in the case of the existence of a pre dual appropriate specializations of these characterizations are also reviewed

an elemental characterization of strong primeness in lie algebras abstract in this paper we prove that a lie algebra l is strongly prime if and only if x y l 0 for every nonzero elements x y l as a consequence we give an elementary proof without the classification theorem of strongly prime jordan algebras of the fact that a linear jordan algebra or jordan pair t is strongly prime if and only if x t y 0 for every x y t moreover we prove that the jordan algebras at nonzero jordan elements of strongly prime lie algebras are strongly prime

central kernels of subspaces of jb triples abstract an investigation of the norm central kernel k n l of an arbitrary norm closed subspace l of a jb triple and the central kernel k l of a weak closed subspace l of a jbw triple is carried out it is shown that these geometrically defined objects have purely algebraic characterizations the results providing new information about c algebras and w algebras

operators with singular continuous spectrum ii rank one operators for an operator a with cyclic vector we studya p wherep is the rank one projection onto multiples of if spec a anda has no a c spectrum we prove thata p has purely singular continuous spectrum on for a denseg of s

on grassmannians associated with jb triples then is a complex lie group that has precisely n 1 orbits e0 en in e each er is the locally closed complex submanifold of all matrices of rank r clearly er 1 is in the closure of er for every 1 r n and en is the unique open orbit for every pair of integers p q 0 let gp q be the grassmannian of all p planes in cp q then gp q is a compact symmetric hermitian manifold of dimension pq holomorphically equivalent to gq p every er is in a canonical way a equivariant holomorphic fibre bundle

the structure of strongly prime quadratic jordan algebras abstract we extend the structure theory for strongly prime jordan algebras of arbitrary dimension to quadratic algebras of characteristic 2 we show that such j are either 1 hermitian forms h 0 a j h q a lying between an ample subspace of hermitian elements in a prime associative algebra a and those in its martindale ring of quotients q a 2 clifford forms with a scalar extension j j which is an algebra j j q 1 of a nondegenerate quadratic from q with basepoint 1 or 3 albert forms with a scalar extension j j which is a 27 dimensional split albert algebra j h 3 k of 3 3 hermitian matrices over an 8 dimensional split octonion algebra k as a consequence the simple jordan algebras of arbitrary dimension are either hermitian h 0 a for simple a or clifford forms in j q 1 or are albert algebras in particular our methods give an idempotent free classification of all simple finite dimensional algebras which are i special the key to this characterization is the existence of zel manov polynomials in the free special jordan algebra which are both hermitian polynomials whose values always look like hermitian elements and at the same time clifford polynomials nontrivial on 3 3 hermitian matrices hence on special algebras with 3 interconnected idempotents if a zel manov polynomial does not vanish on j then j is of hermitian type and if it does vanish on j then j is of clifford type one example of such a polynomial is q48 p16 x1 y1 z1 w1 p16 x2 y2 z2 w2 p16 x3 y3 z3 w3 for p16 d2x y z 2 dx y w dx y w dx y z x y z thus the structure of jordan algebras depends very directly on polynomial identities and commutators

herstein s theorems and simplicity of hermitian jordan systems abstract in this paper we extend herstein s first construction relating associative and jordan ideals to pairs and triple systems as a consequence we show that an associative pair or triple system is simple if and only if its jordan symmetrization is simple we also generalize herstein s second construction to ample subsystems of associative algebras pairs and triple systems which provides information on their simplicity when the associative structure is simple

entropy production in open volume preserving systems we describe a mechanism leading to positive entropy production in volume preserving systems under nonequilibrium conditions we consider volume preserving systems sustaining a diffusion process like the multibaker map or the lorentz gas a continuous flux of particles is imposed across the system resulting in a steady gradient of concentration in the limit where such flux boundary conditions are imposed at arbitrarily separated boundaries for a fixed gradient the invariant measure becomes singular for instance in the multibaker map the limit invariant measure has a cumulative function given in terms of the nondifferentiable takagi function because of this singularity of the invariant measure the entropy must be defined as a coarse grained entropy instead of the fined grained gibbs entropy which would require the existence of a regular measure with a density the coarse grained entropy production is then shown to be asymptotically positive and moreover given by the entropy production expected from irreversible thermodynamics

on the extension of isometries between the unit spheres of von neumann algebras abstract we prove that every surjective isometry between the unit spheres of two von neumann algebras admits a unique extension to a surjective real linear isometry between these two algebras

isometries of non self adjoint operator algebras abstract we study isometries of certain non self adjoint operator algebras by means of the structure of the complete holomorphic vector fields on their unit balls and the associated partial jordan triple products we show that isometries of nest sub algebras of b h are of the form t utw or t ujt jw where u w are suitable unitary operators and j a fixed involution of h

horoballs and iteration of holomorphic maps on bounded symmetric domains abstract given a fixed point free compact holomorphic self map f on a bounded symmetric domain d which may be infinite dimensional we establish the existence of a family h 0 of convex f invariant domains at a point in the boundary d of d which generalises completely wolff s theorem for the open unit disc in c further we construct horoballs at and show that they are exactly the f invariant domains when d is of finite rank consequently we show in the latter case that the limit functions of the iterates f n with weakly closed range all accumulate in one single boundary component of d

the alternative dunford pettis property on projective tensor products a banach space x has the dunford pettis property dpp if and only if whenever xn and pn are weakly null sequences in x and x respectively we have pn xn 0 freedman introduced a stricly weaker version of the dpp called the alternative dunford pettis property dp1 a banach space x has the dp1 if whenever xn x weakly in x with kxnk kxk and xn is weakly null in x we have that xn xn 0 the authors study the dp1 on projective tensor products of c algebras and jb triples their main result theorem 3 5 states that if x and y are banach spaces such that x contains an isometric copy of c0 and y contains an isometric copy of c 0 1 then x y the projective tensor product of x and y does not have the dp1 as a corollary they get that if x and y are jb triples such that x is not reflexive and y contains 1 then x y does not have the dp1 furthermore if a and b are infinite dimensional c algebras then a b has the dpp if and only if a b has the dp1 if and only if both a and b have the dpp and do not contain 1

measures of weak non compactness in preduals of von neumann algebras and jbw triples abstract we prove among other results that three standard measures of weak non compactness coincide in preduals of jbw triples this result is new even for preduals of von neumann algebras we further provide a characterization of jbw triples with strongly wcg predual and describe the order of seminorms defining the strong topology as a byproduct we improve a characterization of weakly compact subsets of a jbw triple predual providing so a proof for a conjecture open for almost eighteen years on weakly compact operators from a jb triple into a complex banach space

anderson localization for one and quasi one dimensional systems we prove almost sure exponential localization of all the eigenfunctions and nondegeneracy of the spectrum for random discrete schrodinger operators on one and quasi one dimensional lattices this paper provides a much simpler proof of these results than previous approaches and extends to a much wider class of systems we remark in particular that the singular continuous spectrum observed in some quasiperiodic systems disappears under arbitrarily small local perturbations of the potential our results allow us to prove that e g for strong disorder the smallest positive lyapunov exponent of some products of random matrices does not vanish as the size of the matrices increases to infinity

microscopic chaos and reaction diffusion processes in the periodic lorentz gas we apply the hypothesis of microscopic chaos to diffusion controlled reaction which we study in a reactive periodic lorentz gas the relaxation rate of the reactive eigenmodes is obtained as eigenvalue of the frobenius perron operator which determines the reaction rate the cumulative functions of the eigenstates of the frobenius perron operator are shown to be generalizations of lebesgue s singular continuous functions for small enough densities of catalysts the reaction is controlled by the diffusion a random walk model of this diffusion controlled reaction process is presented which is used to study the dependence of the reaction rate on the density of catalysts

2 local triple homomorphisms on von neumann algebras and jbw triples abstract we prove that every not necessarily linear nor continuous 2 local triple homomorphism from a jbw triple into a jb triple is linear and a triple homomorphism consequently every 2 local triple homomorphism from a von neumann algebra respectively from a jbw algebra into a c algebra respectively into a jb algebra is linear and a triple homomorphism

lie algebras graded by 3 graded root systems and jordan pairs covered by grids let r be an irreducible root system a lie algebra l is called graded by r if l is graded with grading group the root lattice of r such that the only nonzero homogeneous subspaces of l have degree 0 or a root in r the grading is induced by the adjoint action of a split cartan subalgebra of a finite dimensional simple lie subalgebra of l with root system r and l is generated by the homogeneous subspaces of nonzero degree this class of lie algebras was introduced and studied by s berman and r moody in invent math 108 1992 where in particular a classification up to central equivalence is given in the simply laced case the doubly laced cases have recently been classified by g benkart and e zelmanov let r be a 3 graded root system i e r is not of type e 8 f 4 or g 2 in this paper lie algebras graded by r are described in a unified way without case by case considerations namely it is shown that a lie algebra l is 3 graded if and only if l is a central extension of the tits kantor koecher algebra of a jordan pair covered by a grid whose associated 3 graded root system is isomorphic to r this result is then used to classify lie algebras graded by r we give the classification of jordan pairs covered by a grid and describe their tits kantor koecher algebras one of the advantages of this approach is that it works over rings containing 1 2 and 1 3 and also for infinite root systems another application is the description of slodowy s intersection matrix algebras arising from multiply affinized cartan matrices

instability of dense point spectrum under finite rank perturbations we prove that if a is a self adjoint operator and r a non negative finite rank operator whose range is cyclic for a then for a generic in the baire sense t in each eigenvalue of the operator has a neighborhood containing no other eigenvalues

on the structure of c0 semigroups of holomorphic caratheodory isometries in hilbert space abstract we establish closed formulas for all strongly continuous one parameter semigroups of holomorphic caratheodory isometries of the unit ball of a hilbert space in terms of spectral resolutions of skew self adjoint dilations related to the reich shoikhet nonlinear infinitesimal generator

iteration of holomorphic maps on lie balls abstract we investigate iterations of fixed point free holomorphic self maps on a lie ball of any dimension where a lie ball is a bounded symmetric domain and the open unit ball of a spin factor which can be infinite dimensional we describe the invariant domains of a holomorphic self map f on a lie ball d when f is fixed point free and compact and show that each limit function of the iterates f n has values in a one dimensional disc on the boundary of d we show that the mobius transformation g a induced by a nonzero element a in d may fail the denjoy wolff type theorem even in finite dimension we determine those which satisfy the theorem