boundary singularity of poisson and harmonic bergman kernels abstract we give a complete description of the boundary behaviour of the poisson kernel and the harmonic bergman kernel of a bounded domain with smooth boundary which in some sense is an analogue of the similar description for the usual bergman kernel on a strictly pseudoconvex domain due to fefferman our main tool is the boutet de monvel calculus of pseudodifferential boundary operators and in fact we describe the boundary singularity of a general potential trace or singular green operator from that calculus

fundamental group of simple c algebras with unique trace abstract we introduce the fundamental group f a of a unital simple c algebra a with a unique normalized trace we compute fundamental groups f a of several nuclear or non nuclear c algebras a k theoretical obstruction enables us to compute the fundamental group easily our study is essentially based on the computation of picard groups by kodaka

extensions of pure states and projections of norm one abstract we show that the extension property for pure states of a c subalgebra b of a c algebra a leads to the existence of a projection of norm one r a b in the case where b is liminal with hausdorff primitive ideal space furthermore r is given by a dixmier process in which the averaging is effected by a group of unitary elements in the centre of the multiplier algebra m b these results generalize earlier work of j anderson and the author for the case when b is a masa of a various applications are given in the context of inductive limit algebras such as af algebras and more generally kumjian s ultraliminary c algebras

double integral characterizations of harmonic bergman spaces abstract recently li et al have characterized except for a critical case the weighted bergman spaces over the complex ball by means of integrability conditions of double integrals associated with difference quotients of holomorphic functions in this paper we extend those characterizations to the case of weighted harmonic bergman spaces over the real ball and complement their results by providing a characterization for the missing critical case we also investigate the possibility of extensions to the half space setting our observations reveal an interesting half space phenomenon caused by the unboundedness of the half space

harmonic bergman functions on half spaces we study harmonic bergman functions on the upper half space of rn among our main results are the bergman projection is bounded for the range 1 p oo certain nonorthogonal projections are bounded for the range 1 p oo the dual space of the bergman ll space is the harmonic bloch space modulo constants harmonic conjugation is bounded on the bergman spaces for the range 1 p oo the bergman norm is equivalent to a normal derivative norm as well as to a tangential derivative norm

symmetries of the car algebra a automorphism of period two of the uhf c algebra of type 2 is constructed for which the fixed point algebra is not approximately finite dimensional the construction also yields a diagonal maximal commutative c subalgebra whose spectrum is not totally disconnected variations and consequences of the construction are discussed

mean dimension and ah algebras with diagonal maps mean dimension for ah algebras with diagonal maps is introduced it is shown that if a simple unital ah algebra with diagonal maps has mean dimension zero then it has strict comparison on positive elements in particular the strict order on projections is determined by traces moreover a lower bound of the mean dimension is given in term of toms comparison radius using classification results if a simple unital ah algebra with diagonal maps has mean dimension zero it must be an ah algebra without dimension growth two classes of ah algebras with diagonal maps are shown to have mean dimension zero the class of ah algebras with at most countably many extremal traces and the class of ah algebras with numbers of extreme traces which induce same state on the k0 group being uniformly bounded in particular this class includes ah algebras with real rank zero

the generalized berg theorem and bdf theorem let a be a separable simple af algebra with finitely many extreme traces we give a necessary and sufficient condition for an essentially normal element x e m a i e ir x is normal r m a m a a is the quotient map having the form y a for some normal element y c m a and a e a we also show that a normal element x e m a can be quasidiagonalized if and only if the fredholm index ind a x 0 for all a 0 sp 7r x in the case that a is a simple c algebra of real rank zero with stable rank one and with continuous scale k1 a 0 and ko a has countable rank we show that a normal element x e m a with zero fredholm index can be written as

the corona algebra of the stabilized jiang su algebra abstract let z be the jiang su algebra and k the c algebra of compact operators on an infinite dimensional separable hilbert space we prove that the corona algebra m z k z k has real rank zero we actually prove a more general result

the free vibration of a type of tapered beams this paper studies the vibrational characteristics of tapered beams with continuously varying rectangular cross section of depth and breadth proportional to xs and xt respectively where both s and t are arbitrary real numbers for a truncated beam and arbitrary positive numbers for a sharp ended beam and x is the axial co ordinate measured from the sharp end of the beam the bernoulli euler theory of bending is used to describe the motion of the beam a new set of beam functions are developed as the admissible functions which are the complete solution of the tapered beam under an arbitrary static load expanded into a taylor series the eigenfrequency equation is obtained by the rayleigh ritz method the accuracy is assured from the convergency and comparison studies the effect of the location of the taylor series expanding point on the convergency is discussed the analysis shows that the present approach is convergent for arbitrary truncation factor by taking the midpoint of the beam as the expanding point of the taylor series numerical results are tabulated for three different tapered beams with various boundary conditions and truncation factors it is shown that the eigenfrequencies can be obtained with high accuracy by using only a small number of terms of the static beam functions 2000 elsevier science s a all rights reserved

free vibration analysis of a type of tapered beams by using adomian decomposition method abstract the adomian decomposition method adm is employed in this paper to investigate the free vibrations of tapered euler bernoulli beams with a continuously exponential variation of width and a constant thickness along the length under various boundary conditions based on adm the governing differential equation for the tapered beam becomes a recursive algebraic equation by using the boundary condition equations the dimensionless natural frequencies and corresponding mode shapes can be easily obtained simultaneously the computed results for different boundary conditions and non uniformity ratios are presented the accuracy is assured from the convergence and comparison published results

berezin transform and toeplitz operators on harmonic bergman spaces abstract for an operator which is a finite sum of products of finitely many toeplitz operators on the harmonic bergman space over the half space we study the problem does the boundary vanishing property of the berezin transform imply compactness this is motivated by the axler zheng theorem for analytic bergman spaces but the answer would not be yes in general because the berezin transform annihilates the commutator of any pair of toeplitz operators nevertheless we show that the answer is yes for certain subclasses of operators in order to do so we first find a sufficient condition on general operators and use it to reduce the problem to whether the berezin transform is one to one on related subclasses

diagonality inc algebras soit a une c algebre et a sa les elements hermitiens soit i un ideal ferme separable dans une c algebre a et on suppose que les elements de a sa de spectres finis sont denses dans a sa si a a sa et e 0 alors il existe b a sa diagonal relativement a i et il existe x i sa tel que x e et a b x

on a simple unital projectionless c algebra we construct a unital separable c algebra z as an analog of the hyperfinite type ii 1 factor besides being nuclear simple projectionless and infinite dimensional z has a unique tracial state and is kk equivalent to inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 01i the algebra of complex numbers it is shown that unital endomorphisms on z are approximately inner and that z is isomorphic to the infinite tensor product of its replicas it is also shown that a z a for certain interesting classes of unital simple nuclear c algebras a of real rank zero

c algebras of real rank zero abstract the concept of real rank of a c algebra is introduced as a non commutative analogue of dimension it is shown that real rank zero is equivalent to the previously defined conditions fs and hp and that it is invariant under strong morita equivalence in particular under stable isomorphism real rank zero is also invariant under inductive limits and split extensions and the class may well be regarded as the conceptual completion of the af algebras in some cases notably when the algebra is matroid it is shown that the multiplier algebra also has real rank zero although that is not true in general by a result of g j murphy this implies a weyl von neumann type result for self adjoint multiplier elements in these cases

on the structure of simple c algebras tensored with a uhf algebra ii let d be a simple unital c algebra let b be a uhf algebra and put a b d it is proved that if p q a are projections and p q for all quasitraces on a then p q in the sense of murray and von neumann a more general result involving positive operators in a is also proved if d has finitely many extremal quasi traces and the projections in d k separate these then it is proved that a has real rank zero finally it is proved that provided d is stably finite then each positive state on k0 d lifts to a quasi trace

vibration in the two principal planes of a non uniform beam of rectangular cross section one side of which varies as the square root of the axial co ordinate abstract the transverse vibration of a type of slender beam of continuously varying rectangular cross section is considered in this paper one side of the cross section is constant while the other side is proportional to the square root of the axial co ordinate it is assumed that the beam dimensions are such that application of the euler bernoulli theory of bending is valid thus the vibration in the two principal planes will be uncoupled the two mode shape equations are fourth order linear differential equations with variable coefficients and with regular singularity analytical solutions of the two mode shape equations are derived based on the method of frobenius combinations of ideal clamped pinned sliding and free boundary conditions are considered the sharp end of a complete beam cannot sustain a bending moment or shearing force and hence must always remain free the large end may be clamped pinned sliding or free the frequency equations for a complete beam is the determinant of a 2 2 matrix equated to zero for a truncated beam any combinations of the four boundary conditions is possible and the frequency equations are the determinant of a 4 4 matrix equated to zero the first three dimensionless natural frequencies for vibration in the two principal planes are tabulated for 16 combinations of the four boundary conditions and truncation factors from 0 05 to 0 7 to preserve the accuracy of the frequencies to six figures the results are presented in tabular form it is hoped that they will serve as benchmarks

the ideal property the projection property continuous fields and crossed products abstract let a be the c algebra associated to an arbitrary continuous field of c algebras we give a necessary and sufficient condition for a to have the ideal property and if moreover a is separable we give a necessary and sufficient condition for a to have the projection property some applications of these results are given we also prove that many crossed products of commutative c algebras by discrete amenable groups have the projection property generalizing some of our previous results

abelian strict approximation in aw algebras and weyl von neumann type theorems in this paper for a c algebra a with m m a an aw algebra or equivalently for an essential norm closed two sided ideal a of an aw algebra m we investigate the strict approximability of the elements of m from commutative c subalgebras of a in the relevant case of the norm closed linear span a of all finite projections in a semi finite aw algebra m we shall give a complete description of the strict closure in m of any maximal abelian self adjoint subalgebra masa of a we shall see that the situation is completely different for discrete respectively continuous m in the discrete case for any masa c of a the strict closure of c is equal to the relative commutant c m while in the continuous case under certain conditions concerning the center valued quasitrace of the finite reduced algebras of m satisfied by all von neumann algebras c is already strictly closed thus in the continu ous case no elements of m which are not already belonging to a can be strictly approximated from commutative c subalgebras of a in spite of this pathology of the strict topology in the case of the norm closed linear span of all finite projections of a continuous semi finite aw algebra we shall prove that in general situations including also this case any normal y 2 m is equal modulo a to some x 2 m which belongs to an order theoretical closure of an appropriate commutative c subalgebra of a in other words if we replace the strict topology with order theoretical approximation weyl von neumann berg sikonia type theo rems will hold in substantially greater generality

zero products of toeplitz operators with harmonic symbols on the bergman space of the unit ball in cn we solve the zero product problem for two toeplitz operators with harmonic symbols that have continuous extensions to some part of the boundary in the case where symbols have lipschitz continuous extensions to the boundary we solve the zero product problem for multiple products with the number of factors depending on the dimension n of the underlying space the number of factors is n 3 we also prove a local version of this result but with loss of a factor

berezin transforms on pluriharmonic bergman spaces we show that perhaps surprisingly in several aspects the behaviour of the reproducing kernels of toeplitz operators and of the berezin transform on some weighted pluriharmonic bergman spaces is the same as in the holomorphic case

classical jacobi polynomials closed form solutions for transverse vibrations this paper deals with transverse vibrations of nonuniform homogeneous beams and plates classes of beams and axisymmetrical circular plates whose boundary value problems of free transverse vibrations and free transverse axisymmetrical vibrations respectively can be reduced to an eigenvalue singular problem singularities occur at both ends of orthogonal polynomials are reported exact natural frequencies and jacobi polynomials as exact mode shapes which result directly from eigenvalues and eigenfunctions of eigenvalue singular problems of classical orthogonal polynomials are reported for these classes the above classes of beams and plates hereafter called jacobi classes are given by geometry and boundary conditions the geometry consists of parabolic thickness variation with respect to the axial coordinate for beams and with respect to the radius for plates beams belonging to this class have either one or two sharp ends singularities along with certain boundary conditions plates have zero thickness at zero and outer radii the boundary value problems associated with plates and beams of two sharp ends are free boundary problems two other boundary value problems hinged free and sliding free are reported for beams with one sharp end also exact natural frequencies and mode shapes for uniformly rotating beams with hinged free boundary are reported

toeplitz algebra and hankel algebra on the harmonic bergman space in this paper we completely characterize compact toeplitz operators on the harmonic bergman space by using this result we establish the short exact sequences associated with the toeplitz algebra and the hankel algebra we show that the fredholm index of each fredholm operator in the toeplitz algebra or the hankel algebra is zero

an analogue of the thom isomorphism for crossed products of a c algebra by an action of r abstract in this paper we show the existence and uniqueness of a natural isomorphism oj of kj a with kj 1 a r j z 2 where a r is a c dynamical r system k is the functor of topological k theory and a r is the crossed product of a by the action of r the pimsner voiculescu exact sequence is obtained as a corollary we show that given an invariant trace on a with dual trace gt one has gto 1 u 1 2 i u u for any unitary u in the domain of the derivation of a associated to the action finally we show that the crossed product of c s3 continuous functions on the 3 sphere by a minimal diffeomorphism is a simple c algebra with no nontrivial idempotent

type decomposition for von neumann algebra embeddings this paper establishes a type decomposition theory for embeddings of a von neumann algebra a into a von neumann algebra m by studying projections in a that are semifinite resp abelian relative to m an application of this theory is a complete characterization of the subalgebras a of m that have an n equipartition of the identity i e i k 1npk with projections pk a which are equivalent in m from this follows r v kadison s result amer j math 106 1984 1451 1468 that masas of m always have equipartitions and hence that normal operator valued matrices are diagonalizable a second application is an answer to a question by g k pedersen and e stormer indiana univ math j 23 1973 121 129 on the characterization of g finite projections in discrete crossed products

the sarason sub symbol and the recovery of the symbol of densely defined toeplitz operators over the hardy space abstract while the symbol map for the collection of bounded toeplitz operators is well studied there has been little work on a symbol map for densely defined toeplitz operators in this work a family of candidate symbols the sarason sub symbols is introduced as a means of reproducing the symbol of a densely defined toeplitz operator this leads to a partial answer to a question posed by donald sarason in 2008 in the bounded case the toeplitzness of an operator can be classified in terms of its sarason sub symbols this justifies the investigation into the application of the sarason sub symbols on densely defined operators it is shown that analytic closed densely defined toeplitz operators are completely determined by their sarason sub symbols and it is shown for a broader class of operators that they extend closed densely defined toeplitz operators of multiplication type

trivial k1 flow of af algebras and finite von neumann algebras abstract a c algebra is said to have a trivial k1 flow if k1 b 0 for any hereditary c subalgebra b of m a we prove that if a is a unital af algebra then a has a trivial k1 flow and that if a is a finite von neumann algebra then a k has a trivial k1 flow moreover we prove that if the multiplier algebra of a has fs then the unitary group of b is connected for any hereditary c subalgebra b of m a in addition we prove that if a is either a unital nonunital purely infinite simple c algebra or a nonunital c algebra stably isomorphic to a bunce deddens algebra then k1 b 0 for any hereditary c subalgebra b of m a not contained in a

the small projections property of c algebras abstract we prove a new characterization of rickart c algebras in terms of compact projections we also characterize the small projections property sp for type i c algebras with hausdorff primitive spectrum as an application to group c algebras we identify certain locally compact groups g for which c g has sp finally among other results a characterization of a w algebras is given in terms of sp

heat flow bmo and the compactness of toeplitz operators abstract in this paper it is shown that the berezin toeplitz operator t g is compact or in the schatten class s p of the segal bargmann space for 1 p whenever g s c 0 c n vanishes at infinity or g s l p c n d v respectively for some s with 0 s 1 4 where g s is the heat transform of g on c n moreover we show that compactness of t g implies that g s is in c 0 c n for all s 1 4 and use this to show that for g bmo 1 c n we have g s is in c 0 c n for some s 0 only if g s is in c 0 c n for all s 0 this backwards heat flow result seems to be unknown for g bmo 1 and even g l finally we show that our compactness and vanishing backwards heat flow results hold in the context of the weighted bergman space l a 2 b n d v where the heat flow g s is replaced by the berezin transform b g on l a 2 b n d v for 1

groups quasidiagonality and interpolation by multiplier projections we relate the following conditions on a a unital c algebra a with the fs property a k1 a 0 b every projection in m a a lifts c the general weyl von neumann theorem holds in m a any selfadjoint element h in m a can be written as h a lpi a for some selfadjoint element a in a some bounded real sequence ai and some mutually orthogonal projections pi in a with ez1 pi 1 d m a has fs and e interpolation by multiplier projections holds for any closed projections p and q in a with pq o there is a projection r in m a such that p b 4 a and that a x b if in addition a is stable combining the above results we obtain counterexamples to the conjecture of g k pedersen a has fs m a has fs for example the stabilized buncededdens algebras hence the generalized weyl von neumann theorem does not generally hold in l ha for a unital c algebras with fs

diagonalizing matrices over c x a complete characterization of those compact hausdorff spaces is given such that for every n each normal element in the algebra c x mn of continuous functions from x to mn can be continuously diagonalized the conditions are that x be a sub stonean space with dim x 2 and carries no nontrivial g bundles over any closed subset for g a symmetric group or the circle group in particular diagonalization is assured on every totally disconnected sub stonean space but also on connected spaces of the form y y where y is a simply connected noncompact graph