elastic response of a free half space to random force excitations applied on the boundary abstract a response of an elastic half space to random forces applied normally to the free boundary is studied this paper is the second part of the study we presented in i a shalimova k k sabelfeld the response of an elastic three dimensional half space to random correlated displacement perturbations on the boundary physica a 389 21 2010 4436 4449 where the case of random displacements on the boundary was considered we analyze the white noise excitations in detail and derive explicitly the mean of the elastic energy the strain and displacement correlation tensors simulation algorithms are constructed both for displacement and strain random fields which enables us to calculate any desired statistical characteristics

peirce inner ideals in general position abstract three elements u v and w in the complete lattice i a of weak closed inner ideals in a jbw triple a are said to be in general position when u v form a rigidly collinear pair and u w and v w form orthogonal pairs a complete description of the supremum u v w in i a in terms of the peirce spaces corresponding to u v and w is given for the case in which all three inner ideals are peirce and three other conditions are satisfied by considering an example in the albert jbw triple h 3 o it is shown that none of these is redundant and therefore that the result obtained is the best possible

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

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

multidimensional reaction diffusion equations with white noise boundary perturbations in this paper we study multidimensional stochastic reaction diffusion equations srde s with white noise boundary data more precisely we consider a general srde with robin data to be a white noise field because this boundary data is very irregular we formulate a set of conditions that a random field must satisfy to solve the srde we show that a unique solution exists and we study the boundary layer behavior of the solution this boundary layer analysis reveals some natural restrictions on the reaction term of the srde that ensure that the reaction term does not qualitatively affect the boundary layer the boundary layer analysis also leads to the definition of some functional banach spaces into which are encoded the boundary layer degeneracies and that would be the natural settings for other analyses of the srde of this paper e g large deviations and central limit theorems approximation theorems

a stochastic spectral projection method for solving pdes in domains composed by overlapping discs spheres and half spaces a new mesh free stochastic spectral method based on a spectral inversion of the poisson integral formula is suggested we consider the cases of laplace equation and the system of elasticity equations for domains consisting of overlapping discs half planes spheres and half spaces a randomized projection method we developed in sabelfeld and loshchina 2010 21 is used to solve the system of linear equations approximating the integral equations whose phase space is the intersection surfaces of the domains

long term behavior of polynomial chaos in stochastic flow simulations in this paper we focus on the long term behavior of generalized polynomial chaos gpc and multi element generalized polynomial chaos me gpc for partial differential equations with stochastic coefficients first we consider the one dimensional advection equation with a uniform random transport velocity and derive error estimates for gpc and me gpc discretizations subsequently we extend these results to other random distributions and high dimensional random inputs with numerical verification using the algebraic convergence rate of me gpc finally we apply our results to noisy flow past a stationary circular cylinder simulation results demonstrate that me gpc is effective in improving the accuracy of gpc for a long term integration whereas high order gpc cannot capture the correct asymptotic behavior

on the stability of j homomorphisms abstract the main purpose of this paper is to prove the generalized hyers ulam rassias stability of j homomorphisms between j algebras

a nystrm method for integral equations with fixed singularities of mellin type in weighted lp spaces we consider integral equations of the second kind with fixed singularities of mellin type according to the behavior of the mellin kernel we first determine suitable weighted lp spaces where we look for the solution then for its approximation we propose a numerical method of nystrm type based on a gaussjacobi quadratura formula actually a slight modification of the classical procedure is introduced in order to prove convergence results in weighted lp spaces moreover a preconditioning technique allows us to solve well conditioned linear systems we show the efficiency of the proposed method through some numerical tests

classification of sequentially weakly continuous jb triples let d be the open unit ball of a jb triple a and let aut d be the group of all biholomorphic automorphisms of d it is shown that every element of aut d is sequentially weakly continuous if and only if every primitive ideal of a is a maximal closed ideal and a is a type i jbw triple without infinite spin part implications for general structure theory are explored in particular it is deduced that every jb triple a contains a smallest ideal j for which the sequentially weakly continuous biholomorphic automorphisms of the open unit ball of a j are all linear

a multiscale stochastic finite element method on elliptic problems involving uncertainties in this study a multiscale stochastic finite element method mssfem is developed to resolve scale coupling stochastic elliptic problems based on formulations of a stochastic variational approach and scale bridging multiscale shape functions by employing polynomial chaos expansions and lagrange polynomials stochastic galerkin method and stochastic collocation method are introduced and combined with deterministic multiscale methods i e variational multiscale method and multiscale finite element method the resulting spectral and pseudo spectral stochastic finite element methods are incorporated into the fine and coarse mesh computation of the mssfem a benchmark multiscale model and the numerical experiment based on the formulated mssfem are provided for illustration it is expected that the proposed mssfem can act as a paradigm for solving of general stochastic partial differential equations involving multiscale stochastic data

minimal solutions of three term recurrence relations and orthogonal polynomials we observe that the well known recurrence relation pn x z z a pn z bnp l z for orthogonal polynomials admits a minimal solution if z is outside the spectrum of the mass distribution ds t with respect to which the polynomials are orthogonal and if the moment problem for this distribution is determined the minimal solution indeed is f z m ds t z t and can be computed accurately by means of the author s continued fraction algorithm an application is made to special gauss type quadrature formulas 1 introduction minimal solutions of three term recurrence relations and their computational implications are discussed systematically in 7 effective algorithms for computing minimal solutions have been developed in 7 16 17 and continue to be the subject of further study see e g 14 26 5 2 24 25 3 with these powerful algorithms at hand it seems desirable to delineate large classes of recurrence relations for which the presence of minimal solutions can be ascertained and the minimal solution itself identified even more desirable is an understanding of the deeper reasons for the occurrence of minimal solutions in terms of intrinsic features of the subject area in which they arise few attempts have been made along these lines the work of thacher 22 23 on power series solution of linear differential equations with polynomial coeffi cients may be considered a beginning inasmuch as the presence of minimal solutions of the recurrence relation satisfied by the expansion coefficients is conjectured to be related in a specified way to the type of singularities in the differential equation here we wish to consider the recurrence relation

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

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

multidimensional operator multipliers we introduce multidimensional schur multipliers and characterise them generalising well known results by grothendieck and peller we define a multidimensional version of the two dimensional operator multipliers studied recently by kissin and shulman the multidimensional operator multipliers are defined as elements of the minimal tensor product of several c algebras satisfying certain boundedness conditions in the case of commutative c algebras the multidimensional operator multipliers reduce to continuous multidimensional schur multipliers we show that the multipliers with respect to some given representations of the corresponding c algebras do not change if the representations are replaced by approximately equivalent ones we establish a non commutative and multidimensional version of the characterisations by grothendieck and peller which shows that universal operator multipliers can be obtained as certain weak limits of elements of the algebraic tensor product of the corresponding c algebras

stokes flows under random boundary velocity excitations a viscous stokes flow over a disc under random fluctuations of the velocity on the boundary is studied we give exact karhunen loeve k l expansions for the velocity components pressure stress and vorticity and the series representations for the corresponding correlation tensors both the white noise fluctuations and general homogeneous random excitations of the velocities prescribed on the boundary are studied we analyze the decay of correlation functions in angular and radial directions both for exterior and interior stokes problems numerical experiments show the fast convergence of the k l expansions the results indicate that ignoring the stochastic fluctuations in boundary conditions dramatically underestimates the variance of the velocity and pressure in the interior exterior of the domain

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

hilbert modules in quantum electro dynamics and quantum probability a physical system of the form with a distinguished state on may be described in a natural way on a hilbert module following the ideas of accardi and lu 1 we apply this possibility to a concrete system consisting of a boson field in the vacuum state coupled to a free electron

uniqueness universality and homogeneity of the noncommutative gurarij space we realize the noncommutative gurarij space ng defined by oikhberg as the fraisse limit of the class of finite dimensional 1 exact operator spaces as a consequence we deduce that the noncommutative gurarij space is unique up to completely isometric isomorphism homogeneous and universal among separable 1 exact operator spaces we also prove that ng is the unique separable nuclear operator space with the property that the canonical triple morphism from the universal tro to the triple envelope is an isomorphism we deduce from this fact that ng does not embed completely isometrically into an exact c algebra and it is not completely isometrically isomorphic to a c algebra or to a tro we also provide a canonical construction of ng which shows that the group of surjective complete isometries of ng is universal among polish groups analog results are proved in the commutative setting and more generally for m n spaces in particular we provide a new characterization and canonical construction of the gurarij banach space

on the manifold of tripotents in jb triples the manifold of tripotents in an arbitrary jb triple z is considered a natural affine connection is defined on it in terms of the peirce projections of z and a precise description of its geodesics is given regarding this manifold as a fiber space by neher s equivalence the base space is a symmetric kahler manifold when z is a classical cartan factor and necessary and sufficient conditions are established for connected components of the manifold to admit a riemann structure

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

multipliers on matrix ordered operator spaces and some k groups abstract matrix ordered operator spaces are non commutative banach spaces equipped with a non commutative order examples include c algebras as well as their duals in this article we define and intrinsically characterize the multiplier algebra for this class of spaces and briefly tackle the problem of extending k theory to this context

compatible subtriples of jordan triples abstract the purpose of this paper is to extend the notion of compatibility of tripotents in an anisotropic jordan triple a to that of subtriples of a for a subtriple b of a define the kernel ker b and the annihilator b of b to be the subsets a a b a b 0 and a a b a a 0 respectively the peirce spaces b i i 0 1 2 of b are defined in terms of the kernel and the annihilator by b 0 b b 1 ker b ker b and b 2 b a pair b c of subtriples of a is said to be compatible if a coincides with i j 0 1 2 b i c j the subtriple b is said to be self compatible if it is compatible with itself a self compatible subtriple b is complemented in that b ker b coincides with a which implies that b is an inner ideal in a it follows that a pair u v of tripotents in a is compatible if and only if the ranges im p 2 u im p 2 v of the peirce projections p 2 u and p 2 v form a compatible pair of subtriples moreover for any tripotent u im p 2 u is a self compatible subtriple of a for the special case of a jbw triple a it is shown that a subtriple i is compatible with every self compatible subtriple j if and only if i is a complemented ideal in a these results are then applied to abelian jbw triples w algebras and hilbert spaces

high order methods for weakly singular integral equations with nonsmooth input functions to solve one dimensional linear weakly singular integral equations on bounded intervals with input functions which may be smooth or not we propose to introduce first a simple smoothing change of variable and then to apply classical numerical methods such as product integration and collocation based on global polynomial approximations the advantage of this approach is that the order of the methods can be arbitrarily high and that the associated linear systems one has to solve are very well conditioned

high order methods for linear functionals of solutions of second kind integral equations the authors show that linear functionals e g inner products or point functionals of solutions of second kind fredholm integral equations may be found within o 1 n 2r by very simple computational schemes using the nystrom or quadrature method based on piecewise polynomials of order r on an n 1 point mesh our theory covers a class of nonsmooth wiener hopf type equations and applications include the calculation of crack energy and stress intensity factors in certain linear elastic fracture problems and the use of the boundary integral method to compute various superconvergent solutions to boundary value problems in polygonal domains a proof of the uniform convergence of nystrom s method for certain boundary integral equations on polygonal domains is also included

a nystrom method for boundary integral equations in domains with corners we give a convergence and error analysis for a nystrom method on a graded mesh for the numerical solution of boundary integral equations for the harmonic dirichlet problem in plane domains with corners

collocation quadrature methods and fast summation for cauchy singular integral equations with fixed singularities abstract basing on recent results on the stability of collocation methods applied to cauchy singular integral equations with additional fixed singularities we give necessary and sufficient conditions for the stability of collocation quadrature methods for such equations these methods have the advantage that the respective system of equations has a very simple structure and allows to apply fast summation methods which results in a fast algorithm with o n log n complexity we present numerical results of the application of the proposed collocation quadrature methods to the notched half plane problem of two dimensional elasticity theory

comparative analysis of multiscale gaussian random field simulation algorithms abstract we analyze and compare the efficiency and accuracy of two simulation methods for homogeneous random fields with multiscale resolution we consider in particular the fourier wavelet method and three variants of the randomization method a without any stratified sampling of wavenumber space b with stratified sampling of wavenumbers with equal energy subdivision c with stratified sampling with a logarithmically uniform subdivision we focus primarily on fractal gaussian random fields with kolmogorov type spectra previous work has shown that variants a and b of the randomization method are only able to generate a self similar structure function over three to four decades with reasonable computational effort by contrast variant c along with the fourier wavelet method is able to reproduce accurate self similar scaling of the structure function over a number of decades increasing linearly with computational effort for our examples we will show that nine decades can be reproduced we provide some conceptual and numerical comparison of the various cost contributions to each random field simulation method we find that when evaluating ensemble averaged quantities like the correlation and structure functions as well as some multi point statistical characteristics the randomization method can provide good accuracy with less cost than the fourier wavelet method the cost of the randomization method relative to the fourier wavelet method however appears to increase with the complexity of the random field statistics which are to be calculated accurately moreover the fourier wavelet method has better ergodic properties and hence becomes more efficient for the computation of spatial rather than ensemble averages which may be important in simulating the solutions to partial differential equations with random field coefficients

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

weak exactness for dual operator spaces we introduce a new tensor product circle times sigma lambda and study the weak condition c which is also called weak exactness for dual operator spaces our definition of weak condition c is equivalent to kirchberg s notion of weak exactness in the case of von neumann algebras we also study the connection of weak exact w tros with their linking von neumann algebras and study the structure of exact respectively nuclear w tros c 2007 elsevier inc all rights reserved

numerical simulation of randomly forced turbulent flows several authors have proposed studying randomly forced turbulent flows e g e a novikov soviet physics jetp 20 5 1290 1965 more recently theoretical investigations e g renormalization group have focused on white noise forced navier stokes equations v yakhot and s a orszag j sci comput 1 1 3 1986 the present article aims to provide an appropriate numerical method for the simulation of randomly forced turbulent systems the spatial discretization is based on the classical fourier spectral method the time integration is performed by a second order runge kutta scheme the consistency of an extension of this scheme to treat additive noise stochastic differential equations is proved the random number generator is based on lagged fibonacci series results are presented for two randomly forced problems the burgers and the incompressible navier stokes equations with a white noise in time forcing term characterized by a power law correlation function in spectral space a variety of statistics are computed for both problems including the structure functions the third order structure functions are compared with their exact expressions in the inertial subrange the influence of the dissipation mechanism viscous or hyperviscous on the inertial subrange is discussed in particular probability density functions of velocity increments are computed for the navier stokes simulation finally for both burgers and navier stokes problems our results support the view that random sweeping is the dominant effect of the large scale motion on the small scales

semigroups of holomorphic isometries the aim of the lectures was that of giving a reasonably self contained exposition of the current status of the theory of semigroups of holomorphic isometries and of groups of holomorphic automorphisms acting on hyperbolic domains assuming as a prerequisite only a rather rudimentary knowledge of frechet holomorphy in complex banach spaces this character quite far from any purpose of providing an exhaustive exposition of the geometry of hyperbolic domains has been preserved in the present report which is an expanded version of the preparatory notes of the lectures systematic expositions of the general theory of invariant metrics of homogeneous domains and of homogeneous banach manifolds may be found in some of the treatises quoted in the list of references at the end of this report after reviewing in the first chapter the basic theory of invariant metrics on the unit disc of the complex field and on domains in complex banach spaces the second chapter deals with holomorphic isometries holomorphic automorphisms and holomorphic families thereof these topics are investigated in the third and fourth chapter in the case of unit balls of complex hilbert spaces and more generally of cartan factors of type one this study sets the stage for the theory of strongly continuous semigroups of linear isometries acting on spaces endowed with an indefinite metric and more specifically on krein and pontryagin spaces this theory is exposed in the second part of the third chapter of the present report

finite tripotents and finite jbw triples abstract we study two natural preorders on the set of tripotents in a jb triple defined in terms of their peirce decomposition and weaker than the standard partial order we further introduce and investigate the notion of finiteness for tripotents in jbw triples which is a natural generalization of finiteness for projections in von neumann algebras we analyze the preorders in detail using the standard representation of jbw triples we also provide a refined version of this representation in particular a decomposition of any jbw triple into its finite and properly infinite parts since a jbw algebra is finite if and only if the extreme points of its unit ball are just unitaries our notion of finiteness differs from the concept of modularity widely used in jordan structures so far the exact relationship of these two notions is clarified in the last section

a collocation method for the generalized airfoil equation for an airfoil with a flap we are concerned with the numerical solution of the generalized airfoil equation for an airfoil with a flap by means of global algebraic polynomial approximants this problem has been considered in a recent paper by monegato and sloan siam j numer anal 34 1997 pp 2288 2305 where the authors proved the stability and convergence of a galerkin method based on high order polynomials they also presented very promising numerical results for the corresponding collocation method but left the theoretical results of stability and convergence as an open problem we have succeeded in proving the stability and convergence properties of this collocation method by slightly modifying it in the neighborhood of the flap the rate of convergence we have derived for our collocation method is very similar to that of the above galerkin method

the orthogonal lie algebra of operators ideals and derivations abstract we study in this paper the infinite dimensional orthogonal lie algebra o c which consists of all bounded linear operators t on a separable infinite dimensional complex hilbert space h satisfying c t c t where c is a conjugation on h by employing results from the theory of complex symmetric operators and skew symmetric operators we determine the lie ideals of o c and their dual spaces we study derivations of o c and determine their spectra these results complete some results of p de la harpe and provide interesting contrasts between o c and the algebra b h of all bounded linear operators on h

on injectivity and nuclearity for operator spaces an injective operator space v which is dual as a banach space has the form er 1 e where r is an injective von neumann algebra and where e is a projection in r this is used to show that an operator space v is nuclear if and only if it is locally reflexive and v ast ast is injective it is also shown that any exact operator space is locally reflexive

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

the wiener askey polynomial chaos for stochastic differential equations we present a new method for solving stochastic differential equations based on galerkin projections and extensions of wiener s polynomial chaos specifically we represent the stochastic processes with an optimum trial basis from the askey family of orthogonal polynomials that reduces the dimensionality of the system and leads to exponential convergence of the error several continuous and discrete processes are treated and numerical examples show substantial speed up compared to monte carlo simulations for low dimensional stochastic inputs

peirce inner ideals in jordan triples abstract a subspace j of an anisotropic jordan triple a is said to be an inner ideal if the subspace j a j is contained in j an inner ideal j in a is said to be complemented if a is equal to the sum of j and the kernel ker j of j defined to be the subspace of a consisting of elements a in a for which j a j is equal to 0 the annihilator j of an inner ideal j in a is the inner ideal consisting of elements a in a such that j a a is equal to 0 when both j and j are complemented a can be decomposed into the direct sum of j ker j ker j and j modulo six of the generalized peirce relations this decomposition is a grading of a of peirce type since an inner ideal in a jbw triple is complemented if and only if it is weak closed the result described above applies to all weak closed inner ideals j in a jbw triple a furthermore it can be shown that in this case all except five of the generalized peirce relations hold and an example is given of a weak closed inner ideal in a jbw triple for which all five fail to hold thereby showing that the result is the best possible it is also shown that the condition that a weak closed inner ideal in a jbw triple a leads to a grading of a which is of peirce type is equivalent to several other conditions all of a topological rather than algebraic nature these results are applied to w algebras spin triples and the bi cayley triple

holomorphic mappings of domains in operator spaces our object is to give an overview of some basic results about holomorphic mappings of circular domains in various spaces of operators we begin by considering c algebras and pass to j algebras and other spaces when this seems natural our first result is a simple extension of the maximum principle where the unitary operators play the role of the unit circle we illustrate the power of this result by deducing some classical theorems of functional analysis in a straightforward way next we apply cartan s uniqueness theorem to determine biholomorphic mappings and to show that linear mappings between certain operator domains are jordan isomorphisms this motivates the discussion of homogeneous domains our first examples of homogeneous domains are the open unit balls of j algebras which include all the classical domains next we discuss some affinely homogeneous upper half planes in spaces of operators called operator siegel domains of genus 2 although these are always holomorphically equivalent to a bounded domain they are as far as i know not necessarily holomorphically equivalent to a ball our last examples are the domains of linear fractional transformations these are symmetric affinely homogeneous domains which are never holomorphically equivalent to a bounded domain finally we show how certain extensions of the riemann removable singularity theorem allow us to determine the automorphisms of domains where an indefinite operator valued form is positive this includes the operator analogue of the exterior of the open unit disc

on polynomial collocation for second kind integral equations with fixed singularities of mellin type we consider a polynomial collocation for the numerical solution of a second kind integral equation with an integral kernel of mellin convolution type using a stability result by junghanns and one of the authors we prove that the error of the approximate solution is less than a logarithmic factor times the best approximation and using the asymptotics of the solution we derive the rates of convergence finally we describe an algorithm to compute the stiffness matrix based on simple gaus quadratures and an alternative algorithm based on a recursion in the spirit of monegato and palamara orsi all together an almost best approximation to the solution of the integral equation can be computed with n2 log n 2 resp n2 operations where n is the dimension of the polynomial trial space

facial structure in operator algebra theory we give a complete description of the closed faces in twelve kinds of convex sets that appear in operator algebra theory these consist of positive parts of unit balls for c algebras and their dual spaces and for von neumann algebras and their pre duals of self adjoint parts of unit balls in the same four classes and finally of general unit balls in the four classes all these faces are shown to be semi exposed and naturally paired with a polar face in the dual or pre dual space

local facial structure and norm exposed faces of the unit ball in a jb triple abstract each tripotent u in the bidual a of a jb triple a compact relative to a gives rise to a complex banach space p 2 u a with bidual the jbw algebra a 2 u that is a weak closed subtriple of a using the fact that the family of tripotents in the jbw algebra a 2 u compact relative to p 2 u a coincides with the family of tripotents in a 2 u compact relative to a the facial structure of the unit balls in p 2 u a and its dual a 2 u the predual of a 2 u is revealed the jbw algebra b u that is the self adjoint part of the jbw algebra a 2 u is the bidual of the unital gm space b u that consists of the space of all real valued weak continuous affine functions on the normal state space of a 2 u it is therefore possible to investigate the real local facial structure of the unit balls in b u b u and b u some of the results obtained are applied to the problem of identifying the norm exposed faces of the unit ball a 1 in a it is shown that both locally and globally the norm exposed faces of a 1 are those corresponding to compact support tripotents of elements of norm one in the dual space a of a

ordered c ast modules in this first part of a study of ordered operator spaces we develop the basic theory of ordered c bimodules a crucial role is played by open tripotents a jb triple variant of akemann s notion of open projection

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

stochastic analysis of an elastic 3d half space respond to random boundary displacements exact results and karhunen loeve expansion a stochastic response of an elastic 3d half space to random displacement excitations on the boundary plane is studied we derive exact results for the case of white noise excitations which are then used to give convolution representations for the case of general finite correlation length fluctuations of displacements prescribed on the boundary solutions to these elasticity problem are random fields which appear to be horizontally homogeneous but inhomogeneous in the vertical direction this enables us to construct explicitly the karhunen loeve k l series expansion by solving the eigen value problem for the correlation operator simulation results are presented and compared with the exact representations derived for the displacement correlation tensor this paper is a complete 3d generalization of the 2d case study we presented in sabelfeld and shalimova j stat phys 132 6 1071 1095 2008

local properties of ternary rings of operators and their linking c algebras abstract we show that some local properties such as nuclearity exactness and local reflexivity of ternary rings of operators tros are closely related to the local properties of their linking c algebras we also show some equivalent conditions for nuclear tros and show that haagerup s decomposition property for completely bounded maps and pisier s norm can be naturally generalized to tros

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

automatic continuity of biorthogonality preservers between compact c algebras and von neumann algebras abstract we prove that every biorthogonality preserving linear surjection between two dual or compact c algebras or between two von neumann algebras is automatically continuous

linear maps on c algebras which are derivations or triple derivations at a point abstract we prove new results about generalized derivations on c algebras by considering the triple product a b c 2 1 a b c c b a we introduce the study of linear maps which are triple derivations or triple homomorphisms at a point we prove that a continuous linear map t on a unital c algebra is a generalized derivation whenever it is a triple derivation at the unit element if we additionally assume t 1 0 then t is a derivation and a triple derivation furthermore a continuous linear map on a unital c algebra which is a triple derivation at the unit element is a triple derivation similar conclusions are obtained for continuous linear maps which are derivations or triple derivations at zero we also give an automatic continuity result that is we show that generalized derivations on a von neumann algebra and linear maps on a von neumann algebra which are derivations or triple derivations at zero are all continuous even if not assumed a priori to be so

complementary inner ideals in jbw triples abstract the annihilator l of a subspace l of a jbw triple a consists of the elements a in a for which l a a is equal to 0 the kernel ker l of l consists of those elements a in a for which l a l is equal to 0 and the inner ideal inid l in a associated with l consists of the elements a in a for which a l a is equal to 0 and l a a is contained in l a weak closed subspace j is said to be an inner ideal in a if j a j is contained in j in which case a j j 1 j where j 1 is the intersection of the kernels of j and j the inner ideal inid j in a associated with a weak closed inner ideal j in a forms a complementary weak closed inner ideal to j it turns out that inid j is compatible with j and coincides with inid j k j m j in the case where j is a peirce inner ideal in a by completely identifying inid j it is shown that inid j is a peirce inner ideal in a and the inner ideal inid inid j in a associated with inid j is equal to j

the response of an elastic three dimensional half space to random correlated displacement perturbations on the boundary abstract the response of an elastic half space to random excitations of displacements on the boundary under the condition of no shearing forces is studied we analyze the white noise excitations and general random fluctuations of displacements prescribed on the boundary we consider the case of partially ordered defects on the boundary whose positions are governed by an exponential cosine type correlation function the analysis is based on a poisson type integral formula which we derive here for the case of zero shearing forces on the boundary we obtain exact representations for the displacement correlation tensor and the karhunen loeve expansion for the solution of the lame equation itself and analyze some features of the correlation structure of the displacements the monte carlo technique developed can be applied to a wide class of differential equations with random boundary conditions

the λ function in jb triples abstract we discuss the function in the general setting of j b triples several results connecting the function with the distance of a vector to the brown pedersen s quasi invertible elements and extreme convex decompositions have been obtained for j b triples these include j b triple analogues of some related c algebra results due to m rordam l brown and g pedersen

bicircular projections on some matrix and operator spaces a projection on a complex banach space is bicircular if its linear combinations with the complementary projection having coefficients of modulus one are isometries such projections are always bicontractive in this paper we prove structure theorems for bicircular projections acting on the spaces of the full operator algebra symmetric operators and antisymmetric operators

inner ideals and facial structure of the quasi state space of a jb algebra abstract in this paper we relate the geometric structure of the quasi state space a 1 of a jb algebra a to the algebraic structure of a we prove that each non empty w closed face f of a 1 coincides with the set of elements of a that attain their norms at a closed projection p in a uniquely determined by f when a is unital we establish an order anti isomorphism between the complete lattice of w closed faces of a 1 and the complete lattice of norm closed inner ideals of a these results are known for the special case when a is the self adjoint part of a c algebra the proofs use associative techniques and the gelfand naimark representation in the general case such techniques are not available and it is necessary to introduce new techniques including the use of a new inequality of cauchy schwarz type for elements of a

a geometric characterization of structural projections on a jbw triple a structural projection r on a jordan triple a is a linear projection such that for all elements a b and c in a r arbc rabrc the l orthogonal complement g of a subset g of a complex banach space e is the set of elements x in e such that for all elements y in g x y x y a contractive projection p on e is said to be neutral if the condition that px x implies that the elements px and x coincide and is said to be a gl projection if the l orthogonal complement pe of the range pe of p is contained in the kernel ker p of p it is shown that for a jbw triple a with predual a a linear projection r on a is structural if and only if it is the adjoint of a neutral gl projection on a thereby giving a purely geometric characterization of structural projections

elastic half plane under random displacement excitations on the boundary we study in this paper a respond of an elastic half plane to random boundary excitations we treat both the white noise excitations and more generally homogeneous random fluctuations of displacements prescribed on the boundary solutions to these problems are inhomogeneous random fields which are however homogeneous with respect to the longitudinal coordinate this is used to represent the displacements as series expansions involving a complete set of deterministic functions with corresponding random coefficients we construct the karhunen loeve k l series expansion which is based on the eigen decomposition of the correlation operator the k l expansion can be used to calculate the statistical characteristics of other functionals of interest in particular the strain and stress tensors and the elastic energy tensor

a modified nystrom method for integral equations with mellin type kernels the aim of this paper is to propose a new modified nystrom method for the approximation of the solutions of second kind integral equations with fixed singularities of mellin convolution type the stability and the convergence are proved in l 2 spaces and error estimates in l 2 norm are given finally numerical tests showing the effectiveness of the method are presented

subspaces of l h that are invariant abstract a result of choi and effros says how invariant spaces of bounded operators on hilbert space that contain the identity can be abstractly characterized in terms of their order structure the aim here is to dispose of the identity and to prove a similar theorem for spaces of bounded operators that are merely invariant absence of a unit will also permit to deal with duals in a satisfactory way

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