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

rigorous time space trade offs for inverting functions we provide rigorous time space trade offs for inverting any function given a function f we give a time space trade off of t s2 n3 q f where q f is the probability that two random elements taken with replacement are mapped to the same image under f we also give a more general trade off t s3 n3 that can invert any function at any point

the fixed point property in jb triples and preduals of jbw triples abstract we prove that for every member x in the class of real or complex jb triples or preduals of jbw triples the following assertions are equivalent 1 x has the fixed point property 2 x has the super fixed point property 3 x has normal structure 4 x has uniform normal structure 5 the banach space of x is reflexive as a consequence a real or complex c algebra or the predual of a real or complex w algebra having the fixed point property must be finite dimensional

the dunford pettis and the kadec klee properties on tensor products of jb triples we recall that a banach spacex satisfies the dunford pettis property dpp if every weakly compact operator t from x to another banach space is completely continuous i e t maps weakly cauchy sequences into norm convergent sequences the question if the projective tensor product of two banach spaces having the dpp also has this property has focused the attention of several researcher in 1983 m talagrand found a banach space x such that x has the schur property and l1 0 1 e does not satisfy the dpp see 34 four years latter r ryan showed that x y satisfies the dpp and contains no copies of 1 whenever x and y have both properties 33 f bombal and i villanueva prove in 7 see also 6 20 that whenever k1 and k2 are two infinite compact hausdorff spaces then the projective tensor product of c k1 and c k2 has the dpp if and only if k1 and k2 are scattered that is c k1 and c k2 contains no copies of 1 the interesting ideas developed by bombal fernandez and villanueva in 7 6 are the inspiration and the starting point for the present paper in the

octahedral norms and convex combination of slices in banach spaces abstract we study the relation between octahedral norms daugavet property and the size of convex combinations of slices in banach spaces we prove that the norm of an arbitrary banach space is octahedral if and only if every convex combination of w slices in the dual unit ball has diameter 2 which answers an open question as a consequence we get that the banach spaces with the daugavet property and its dual spaces have octahedral norms also we show that for every separable banach space containing l 1 and for every e 0 there is an equivalent norm so that every convex combination of w slices in the dual unit ball has diameter at least 2 e

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

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

channel smoothing efficient robust smoothing of low level signal features in this paper we present a new and efficient method to implement robust smoothing of low level signal features b spline channel smoothing this method consists of three steps encoding of the signal features into channels averaging of the channels and decoding of the channels we show that linear smoothing of channels is equivalent to robust smoothing of the signal features if we make use of quadratic b splines to generate the channels the linear decoding from b spline channels allows the derivation of a robust error norm which is very similar to tukey s biweight error norm we compare channel smoothing with three other robust smoothing techniques nonlinear diffusion bilateral filtering and mean shift filtering both theoretically and on a 2d orientation data smoothing task channel smoothing is found to be superior in four respects it has a lower computational complexity it is easy to implement it chooses the global minimum error instead of the nearest local minimum and it can also be used on nonlinear spaces such as orientation space

solution of the contractive projection problem in this paper we show that the class of j algebras a class of concrete jordan triple systems is stable under the action of norm one projections this result constitutes a general solution to a problem considered by the authors and others specifically our main result is theorem 2 let p be an arbitrary contractive projection defined on a j algebra m then p m is a jordan triple system in the triple product a b c a b c p f ab c t cb a for a b c e p m and p m has a faithful representation as a j algebra

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

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

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

relatively weakly open sets in closed balls of banach spaces and the centralizer we prove that if the centralizer of a banach space x is infinite dimensional then every nonempty relatively weakly open subset of the closed unit ball of x has diameter equal to 2 this result together with a suitable refinement also proven in the paper contains and improves in some cases previously known facts for c algebras jb triples spaces of vector valued continuous functions and spaces of operators

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

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

dynamic perfect hashing upper and lower bounds the dynamic dictionary problem is considered provide an algorithm for storing a dynamic set allowing the operations insert delete and lookup a dynamic perfect hashing strategy is given a randomized algorithm for the dynamic dictionary problem that takes o 1 worst case time for lookups and o 1 amortized expected time for insertions and deletions it uses space proportional to the size of the set stored furthermore lower bounds for the time complexity of a class of deterministic algorithms for the dictionary problem are proved this class encompasses realistic hashing based schemes that use linear space such algorithms have amortized worst case time complexity omega log n for a sequence of n insertions and lookups if the worst case lookup time is restricted to k then the lower bound becomes omega k cdot n 1 k

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

online learning of correspondences between images we propose a novel method for iterative learning of point correspondences between image sequences points moving on surfaces in 3d space are projected into two images given a point in either view the considered problem is to determine the corresponding location in the other view the geometry and distortions of the projections are unknown as is the shape of the surface given several pairs of point sets but no access to the 3d scene correspondence mappings can be found by excessive global optimization or by the fundamental matrix if a perspective projective model is assumed however an iterative solution on sequences of point set pairs with general imaging geometry is preferable we derive such a method that optimizes the mapping based on neyman s chi square divergence between the densities representing the uncertainties of the estimated and the actual locations the densities are represented as channel vectors computed with a basis function approach the mapping between these vectors is updated with each new pair of images such that fast convergence and high accuracy are achieved the resulting algorithm runs in real time and is superior to state of the art methods in terms of convergence and accuracy in a number of experiments

isometries of real hilbert c modules abstract let t v w be a surjective real linear isometry between full real hilbert c modules over real c algebras a and b respectively we show that the following conditions are equivalent a t is a 2 isometry b t is a complete isometry c t preserves ternary products d t preserves inner products e t is a module map when a and b are commutative we give a full description of the structure of t

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

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

structure from motion with wide circular field of view cameras this paper presents a method for fully automatic and robust estimation of two view geometry autocalibration and 3d metric reconstruction from point correspondences in images taken by cameras with wide circular field of view we focus on cameras which have more than 180deg field of view and for which the standard perspective camera model is not sufficient e g the cameras equipped with circular fish eye lenses nikon fc e8 183deg sigma 8 mm f4 ex 180deg or with curved conical mirrors we assume a circular field of view and axially symmetric image projection to autocalibrate the cameras many wide field of view cameras can still be modeled by the central projection followed by a nonlinear image mapping examples are the above mentioned fish eye lenses and properly assembled catadioptric cameras with conical mirrors we show that epipolar geometry of these cameras can be estimated from a small number of correspondences by solving a polynomial eigenvalue problem this allows the use of efficient ransac robust estimation to find the image projection model the epipolar geometry and the selection of true point correspondences from tentative correspondences contaminated by mismatches real catadioptric cameras are often slightly noncentral we show that the proposed autocalibration with approximate central models is usually good enough to get correct point correspondences which can be used with accurate noncentral models in a bundle adjustment to obtain accurate 3d scene reconstruction noncentral camera models are dealt with and results are shown for catadioptric cameras with parabolic and spherical mirrors

tingley s problem through the facial structure of an atomic jbw triple abstract we prove that every surjective isometry between the unit spheres of two atomic jbw triples e and b admits a unit extension to a surjective real linear isometry from e into b this result constitutes a new positive answer to tingley s problem in the jordan setting

real contractive projections on commutative c algebras complex banach jordan triples occurred in the study of bounded symmetric domains in several complex variables and in the study of contractive projections on complex c algebras these spaces are equipped with a ternary product the jordan triple product and are essentially geometric objects in that the linear isometries between them are exactly the linear maps preserving the triple product 13

a simple parallel algorithm for the maximal independent set problem two basic design strategies are used to develop a very simple and fast parallel algorithms for the maximal independent set mis problem the first strategy consists of assigning identical copies o

sparse on line gaussian processes we develop an approach for sparse representations of gaussian process gp models which are bayesian types of kernel machines in order to overcome their limitations for large data sets the method is based on a combination of a bayesian on line algorithm together with a sequential construction of a relevant subsample of the data that fully specifies the prediction of the gp model by using an appealing parameterization and projection techniques in a reproducing kernel hilbert space recursions for the effective parameters and a sparse gaussian approximation of the posterior process are obtained this allows for both a propagation of predictions and bayesian error measures the significance and robustness of our approach are demonstrated on a variety of experiments

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

on the zelmanovian classification of prime jb triples complex jb triples are complex banach spaces endowed with a triple product subjected to suitable conditions of algebraic and analytic nature see section 1 for the definition they were introduced by w kaup in order to provide an algebraic setting for the study of bounded symmetric domains in complex banach spaces the open unit ball of every complex jb triple is a bounded symmetric domain ka1 and every bounded symmetric domain in any complex banach space is bi holomorphically equivalent to the open unit ball of a suitable complex jb triple ka3 fundamental examples of complex jb triples are provided by complex c algebras with triple product defined by xyz x 1 2 xy z zy x 1

little grothendieck s theorem for real jb triples we prove that given a real jb triple e and a real hilbert space h then the set of those bounded linear operators t from e to h such that there exists a norm one functional varphi in e and corresponding pre hilbertian semi norm varphi on e such that