stationarity of operator algebras abstract it is shown that stationary random fields on an arbitrary locally compact group are exactly fourier transforms of orthogonally scattered mappings on the c algebra of the group this result is obtained as a consequence of a theorem stating that each orthogonal form on a c algebra is determined by two functionals on the algebra

semidirect products and reduction in mechanics this paper shows how to reduce a hamiltonian system on the cotangent bundle of a lie group to a hamiltonian system in the dual of the lie algebra of a semidirect product the procedure simplifies unifies and extends work of greene guillemin holm holmes kupershmidt marsden morrison ratiu sternberg and others the heavy top compressible fluids magnetohydrodynamics elasticity the maxwell vlasov equations and multifluid plasmas are presented as examples starting with lagrangian variables our method explains in a direct way why semidirect products occur so frequently in examples it also provides a framework for the systematic introduction of clebsch or canonical variables

symmetry properties of a system of euler type equations for magnetized plasmas we provide all lie point symmetries of a system of partial differential equations of great interest to plasma physics we deduce the corresponding invariant solutions and discuss their physical interpretation we also consider some of its conditional and partial symmetries and obtain other interesting solutions finally we point out that although the system can be cast in divergence form and admits conserved currents it does not admit potential symmetries

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

generalization of solutions of the jacobi pdes associated to time reparametrizations of poisson systems the determination of solutions of the jacobi partial differential equations pdes for finite dimensional poisson systems is considered in particular a novel procedure for the construction of solution families is developed such a procedure is based on the use of time reparametrizations preserving the existence of a poisson structure as a result a method which is valid for arbitrary values of the dimension and the rank of the poisson structure under consideration is obtained in this article two main families of time reparametrizations of this kind are characterized in addition these results lead to a novel application which is also developed namely the global and constructive determination of the darboux canonical form for poisson systems of arbitrary dimension and rank two thus improving the local result provided by darboux theorem for such a case

biseparating maps between operator algebras we prove that a biseparating map between spaces b e and some other banach algebras is automatically continuous and a multiple of an algebra isomorphism

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

weighted composition operators ofc0 x s abstract in this paper we prove that into isometries and disjointness preserving linear maps from c 0 x into c 0 y are essentially weighted composition operators tf h f for some continuous map and some continuous scalar valued function h

stochastic calculus with anticipating integrands we study the stochastic integral defined by skorohod in 24 of a possibly anticipating integrand as a function of its upper limit and establish an extended ito formula we also introduce an extension of stratonovich s integral and establish the associated chain rule in all the results the adaptedness of the integrand is replaced by a certain smoothness requirement

integration par parties dans l espace de wiener et approximation du temps local let be a real valued stochastic process having a continuous local timel u t u 0 t t andxe t e x t t 0 the regularization ofx by means of the convolution with the approximation of unity e the main theorem in this paper theorem 3 5 is a generalization of various results about the approximation for fixedu of the local timel u by means of a convenient normalization of the numbernxe u of crossings of the processxe with the levelu especially this theorem extends to a class of not necessarily markovian continuous martingales a result of this type for one dimensional diffusions due to azais a2 the methods of proof combine some estimations of the moments of the number of crossings with a level of a regular stochastic processes with stochastic analysis techniques based upon integration by parts in the wiener space

new global solutions of the jacobi partial differential equations abstract a new family of solutions of the jacobi partial differential equations for finite dimensional poisson systems is investigated this family is mathematically remarkable as the functional dependences of the solutions appear to be associated to the distinguished invariants of the solutions themselves this kind of poisson structure termed distinguished solutions or d solutions is defined for every nontrivial combination of values of the dimension and the rank and is also determined in terms of functions of arbitrary nonlinearity properties usually not present simultaneously in the already known solution families in addition d solutions display several properties allowing the generation of an infinity of d solutions from a given one which is an uncommon feature in the framework of the jacobi equations furthermore a special family of d solutions complying with the previous requirements is constructively characterized and analyzed examples are discussed focusing on physical implications and including an application for the global construction of the darboux canonical form

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

coadjoint orbits vortices and clebsch variables for incompressible fluids this paper is a study of incompressible fluids especially their clebsch variables and vortices using symplectic geometry and the lie poisson structure on the dual of a lie algebra following ideas of arnold and others it is shown that euler s equations are lie poisson equations associated to the group of volume preserving diffeomorphisms the dual of the lie algebra is seen to be the space of vortices and kelvin s circulation theorem is interpreted as preservation of coadjoint orbits in this context clebsch variables can be understood as momentum maps the motion of n point vortices is shown to be identifiable with the dynamics on a special coadjoint orbit and the standard canonical variables for them are a special kind of clebsch variables point vortices with cores vortex patches and vortex filaments can be understood in a similar way this leads to an explanation of the geometry behind the hald beale majda convergence theorems for vorticity algorithms symplectic structures on the coadjoint orbits of a vortex patch and filament are computed and shown to be closely related to those commonly used for the kdv and the schrodinger equations respectively

perturbed euler top and bifurcation of limit cycles on invariant casimir surfaces abstract analytical perturbations of the euler top are considered the perturbations are based on the poisson structure for such a dynamical system in such a way that the casimir invariants of the system remain invariant for the perturbed flow by means of the poincare pontryagin theory the existence of limit cycles on the invariant casimir surfaces for the perturbed system is investigated up to first order of perturbation providing sharp bounds for their number examples are given

complete orthogonality preservers between c algebras abstract we introduce n orthogonality and completely orthogonality preserving operators between c algebras our main theorem states that every completely orthogonality preserving bounded linear mapping between c algebras is a weighted tro homomorphism we also give several characterisations of tro homomorphisms among triple homomorphisms

generalized stochastic integrals and the malliavin calculus the paper first reviews the skorohod generalized stochastic integral with respect to the wiener process over some general parameter space t and it s relation to the malliavin calculus as the adjoint of the malliavin derivative some new results are derived and it is shown that every sufficiently smooth process ut t t can be decomposed into the sum of a malliavin derivative of a wiener functional and a process whose generalized integral over t vanishes using the results on the generalized integral the bismut approach to the malliavin calculus is generalized by allowing non adapted variations of the wiener process yielding sufficient conditions for the existence of a density which is considerably weaker than the previously known conditions

hamiltonian closures for fluid models with four moments by dimensional analysis fluid reductions of the vlasov ampere equations that preserve the hamiltonian structure of the parent kinetic model are investigated hamiltonian closures using the first four moments of the vlasov distribution are obtained and all closures provided by a dimensional analysis procedure for satisfying the jacobi identity are found two hamiltonian models emerge for which the explicit closures are given along with their poisson brackets and casimir invariants

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

on mappings preserving the sharp and star orders abstract the present paper is devoted to the study of linear maps preserving certain relations such as the sharp partial order and the star partial order in semisimple banach algebras and c algebras

minimal atmospheric finite mode models preserving symmetry and generalized hamiltonian structures abstract a typical problem with the conventional galerkin approach for the construction of finite mode models is to keep structural properties unaffected in the process of discretization we present two examples of finite mode approximations that in some respect preserve the geometric attributes inherited from their continuous models a three component model of the barotropic vorticity equation known as lorenz maximum simplification equations e n lorenz maximum simplification of the dynamic equations tellus 12 3 1960 243 254 and a six component model of the two dimensional rayleigh benard convection problem it is reviewed that the lorenz 1960 model respects both the maximal set of admitted point symmetries and an extension of the noncanonical hamiltonian form nambu form in a similar fashion it is proved that the famous lorenz 1963 model violates the structural properties of the saltzman equations and hence cannot be considered as the maximum simplification of the rayleigh benard convection problem using a six component truncation we show that it is again possible to retain both symmetries and the nambu representation in the course of discretization the conservative part of this six component reduction is related to the lagrange top equations dissipation is incorporated using a metric tensor

the hamiltonian structure of the maxwell vlasov equations morrison 25 has observed that the maxwell vlasov and poisson vlasov equations for a collisionless plasma can be written in hamiltonian form relative to a certain poisson bracket we derive another poisson structure for these equations by using general methods of symplectic geometry the main ingredients in our construction are the symplectic structure on the co adjoint orbits for the group of canonical transformations and the symplectic structure for the phase space of the electromagnetic field regarded as a gauge theory our poisson bracket satisfies the jacobi identity whereas morrison s does not 37 our construction also shows where canonical variables can be found and can be applied to the yang mills vlasov equations and to electromagnetic fluid dynamics

rayleigh benard convection as a nambu metriplectic problem the traditional hamiltonian structure of the equations governing conservative rayleigh benard convection rbc is singular i e its poisson bracket possesses nontrivial casimir functionals we show that a special form of one of these casimirs can be used to extend the bilinear poisson bracket to a trilinear generalized nambu bracket it is further shown that the equations governing dissipative rbc can be written as the superposition of the conservative nambu bracket with a dissipative symmetric bracket this leads to a nambu metriplectic system which completes the geometrical picture of rbc

disjointness preservers of aw algebras abstract in this paper we study bijective linear maps a b between a w algebras preserving either zero products or range orthogonality such a map is automatically continuous and provides an algebra or a algebra isomorphism 1 1 from a onto b our results extend previous works for the case of w algebras and also cover such maps between c algebras satisfying an extra assumption on preserving abelian c subalgebras

separate weak continuity of the triple product in dual real jb triples we prove that if e is a real jb triple having a predual e then e is the unique predual of e and the triple product on e is separately sigma e e continuous

orthogonality preserving c conformal and conformal module mappings on hilbert c modules we investigate orthonormality preserving c conformal and conformal module mappings on full hilbert c modules to obtain their general structure orthogonality preserving bounded module maps t act as a multiplication by an element of the center of the multiplier algebra of the c algebra of coefficients combined with an isometric module operator as long as some polar decomposition conditions for the specific element are fulfilled inside that multiplier algebra generally t always fulfills the equality t x t y 2 x y for any elements x y of the hilbert c module at the contrary c conformal and conformal bounded module maps are shown to be only the positive real multiples of isometric module operators

automatic continuity of orthogonality preservers on a non commutative lp τ space abstract elements a and b of a non commutative l p space associated to a von neumann algebra n equipped with a normal semifinite faithful trace are called orthogonal if l a l b r a r b 0 where l x and r x denote the left and right support projections of x a linear map t from l p n to a normed space y is said to be orthogonality to p orthogonality preserving if t a t b p a p b p whenever a and b are orthogonal in this paper we prove that an orthogonality to p orthogonality preserving linear bijection from l p n 1 p p 2 to a banach space x is automatically continuous whenever n is a separably acting von neumann algebra if n is a semifinite factor not of type i 2 we establish that every orthogonality to p orthogonality preserving linear mapping t l p n x is continuous and invertible whenever t 0 furthermore there exists a positive constant c p 1 p p 2 so that t t 1 c p 2 for every non zero orthogonality to p orthogonality preserving linear mapping t l p n x for p 1 this inequality holds with c p 1 that is t is a multiple of an isometry

approximation du temps local des processus gaussiens stationnaires par regularisation des trajectoires soit x un processus gaussien stationnaire non derivable nous etudions le nombre de passages en zero du processus regularise par convolution sous des hypotheses peu restrictives sur x cette variable convenablement normalisee converge au sens de l2 quand la taille du filtre tend vers zero lorsque x admet un temps local continu la limite obtenue est le temps local

grothendieck s inequalities for real and complex jbw triples we prove that if m 4 1 2 3 and e 0 if v and w are complex jbw triples with preduals v andw respectively and if u is a separately weak continuous bilinear form on v w then there exist norm one functionals 1 2 v and 1 2 w satisfying u x y m u x 2 2 e 2 x 2 1 1 2 y 2 2 e 2 y 2 1 1 2 for all x y v w here for a norm one functional on a complex jb triple v stands for the prehilertian seminorm on v associated to in bf1 we arrive in this grothendieck s inequality through results of c h chu b iochum and g loupias cil and a corrected version of the little grothendieck s inequality for complex jb triples due to t barton and y friedman bf1 we also obtain extensions of these results to the setting of real jb triples 2000 mathematics subject classification 17c65 46k70 46l05 46l10 and 46l70

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

approximation du temps local des surfaces gaussiennes letx be a centered stationary gaussian stochastic process with ad dimensional parameter d 2 f its spectral measure int limits r d x 2 f dx infty x denotes the euclidean norm ofx we consider regularizations of the trajectories ofx by means of convolutions of the formxe t e x t where e stands for an approximation of unity as e tends to zero satisfying certain regularity conditions

classification and casimir invariants of lie poisson brackets abstract we classify lie poisson brackets that are formed from lie algebra extensions the problem is relevant because many physical systems owe their hamiltonian structure to such brackets a classification involves reducing all brackets to a set of normal forms and is achieved partially through the use of lie algebra cohomology for extensions of order less than five the number of normal forms is small and they involve no free parameters we derive a general method of finding casimir invariants of lie poisson bracket extensions the casimir invariants of all low order brackets are explicitly computed we treat in detail a four field model of compressible reduced magnetohydrodynamics

a nonlinear hamiltonian structure for the euler equations abstract the euler equations for inviscid incompressible fluid flow have a hamiltonian structure in eulerian coordinates the hamiltonian operator though depending on the vorticity conservation laws arise from two sources one parameter symmetry groups which are completely classified yield the invariance of energy and linear and angular momenta degeneracies of the hamiltonian operator lead in three dimensions to the total helicity invariant and in two dimensions to the area integrals reflecting the point wise conservation of vorticity it is conjectured that no further conservation laws exist indicating that the euler equations are not completely integrable in particular do not have soliton like solutions

linear disjointness preservers of w algebras in this paper we give a complete description of the structure of zero product and orthogonality preserving linear maps between w algebras in particular two w algebras are isomorphic if and only if there is a bijective linear map between them preserving their zero product or orthogonality structure in two directions it is also the case when they have equivalent linear and left right ideal structures

new solutions of the jacobi equations for three dimensional poisson structures a systematic investigation of the skew symmetric solutions of the three dimensional jacobi equations is presented as a result three disjoint and complementary new families of solutions are characterized such families are very general thus unifying many different and well known poisson structures seemingly unrelated which now appear embraced as particular cases of a more general solution this unification is not only conceptual but allows the development of algorithms for the explicit determination of important properties such as the symplectic structure the casimir invariants and the darboux canonical form which are known only for a limited sample of poisson structures these common procedures are thus simultaneously valid for all the particular cases which can now be analyzed in a unified and more economic framework instead of using a case by case approach in addition the methods developed are valid globally in phase space thus ameliorating the usual scope of darboux reduction which is only of

orthogonality preserving linear maps on c algebras with non zero socles abstract we study orthogonality preserving surjective linear maps from a unital c algebra with non zero socle a to a c algebra in particular we prove that when a has essential socle every biorthogonality preserving surjective linear map t a b is automatically bounded and a jordan isomorphism multiplied by an invertible element

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

automatic continuity of m norms on c algebras abstract elements a and b of a c algebra are called orthogonal a b if a b a b 0 we say that vectors x and y in a banach space x are semi m orthogonal x sm y if x y max x y we prove that every linear bijection t a x where x is a banach space a is either a von neumann algebra or a compact c algebra and t a sm t b whenever a b must be continuous consequently every complete semi m norm on a von neumann algebra or on a compact c algebra is automatically continuous

the minimax principle and related topics in the jordan setting abstract we prove a minimax principle for weakly compact jb triples characterizing geometrically the singular values of an element among the consequences of this principle we present a weyl inequality on the perturbation of the singular values and a cauchy poincare interlacing theorem we also obtain a version of the ky fan maximum principle in the setting of weakly compact jb triples we study perturbations of the spectral resolutions showing that small perturbations of an element produces small perturbations of the corresponding spectral resolutions as a consequence we obtain that weakly compact jb triples satisfy the property that perturbations of a convex combination of elements in the closed unit ball coincide with a convex combination of perturbations of the elements also in the closed unit ball all these results hold true when particularized to weakly compact jb algebras

universal lie algebra extensions and their casimir invariants via commutative structures abstract we consider a special kind of lie algebra extension called universal extension introduced recently we show that there is one to one correspondence with commutative associative algebras we also investigate the casimir invariants for the universal extensions and consider in detail the so called coextension structures arising in the calculation of the casimir functions

perturbation of ell_1 copies in preduals of jbw triples abstract it is known that two normal functionals on a jbw triple are orthogonal i e they have orthogonal support tripotents if and only if they are l orthogonal meaning that they span an isometric copy of l 1 2 this is shown to be stable under small norm perturbations in the following sense if the linear span of the two functionals is isometric up to 0 to l 1 2 then the functionals are less far in norm than e 0 from two orthogonal functionals where e 0 as 0 analogous statements for finitely and even infinitely many functionals hold as well and so does a corresponding statement for non normal functionals

non commutative generalisations of urysohn s lemma and hereditary inner ideals abstract we establish several generalisations of urysohn s lemma in the setting of jb triples which provide full answers to problems 1 12 and 1 13 in fernandez polo and peralta 2007 22 these results extend the previous generalisations obtained by c a akemann g k pedersen and l g brown in the setting of c algebras a generalised kadison s transitivity theorem is established for finite sums of pairwise orthogonal compact tripotents in jbw triples we introduce the notion of positively open tripotent in the bidual of a jb triple as an extension of a concept which was already considered in the setting of ternary rings of operators we investigate the connections appearing between positively open tripotents and hereditary inner ideals