a bishop phelps bollobas type theorem for uniform algebras abstract this paper is devoted to showing that asplund operators with range in a uniform banach algebra have the bishop phelps bollobas property i e they are approximated by norm attaining asplund operators at the same time that a point where the approximated operator almost attains its norm is approximated by a point at which the approximating operator attains it to prove this result we use the weak to norm fragmentability of weak compact subsets of the dual of asplund spaces and we need to observe a urysohn type result producing peak complex valued functions in uniform algebras that are small outside a given open set and whose image is inside a stolz region

the bishop phelps bollobas theorem for operators we prove the bishop phelps bollobas theorem for operators from an arbitrary banach space x into a banach space y whenever the range space has property of lindenstrauss we also characterize those banach spaces y for which the bishop phelps bollobas theorem holds for operators from 1 into y s everal examples of classes of such spaces are provided for instance the bishop phelps bollobas theorem holds when the range space is finite dimensional an l1 space for a finite measure a c k space for a compact hausdorff space k or a uniformly convex banach space

purely infinite partial crossed products let a g be a partial dynamical system we show that there is a bijective correspondence between g invariant ideals of a and ideals in the partial crossed product a rg provided the action is exact and residually topologically free assuming in addition a technical condition automatic when a is abelian we show that a rg is purely infinite if and only if the positive nonzero elements in a are properly infinite in a rg as an application we verify pure infiniteness of various partial crossed products including realisations of the cuntz algebras on oa on and oz as partial crossed products

the daugavet equation for operators on function spaces abstract we prove the norm identity id t 1 t which is known as the daugavet equation for weakly compact operators t on natural function spaces such as function algebras and l 1 predual spaces provided a non discreteness assumption is met we also consider c 0 factorable operators and operators on c spaces

on the polynomial numerical index of the real spaces c0 l1 and l abstract we give a lower bound for the polynomial numerical index of order k for real lush spaces we use this bound to compute the polynomial numerical index of order 2 of the real spaces c 0 l 1 and l finally we present an example of a real banach space x whose polynomial numerical indices are positive while the ones of its bidual are zero

generalizations of cauchy s summation theorem for schur functions cauchy s summation theorem for schur functions is generalized and a number of related results are given the result is applied to a com binatorial problem involving products of pairs of permuations by appeal to properties of the group algebra of the symmetric group in 3 this summation theorem is used to derive a generalization of gessel s 3 result on counting 3 rowed latin rectangles with respect to the number of cycles in each row considered as permuations we also derive proposition 3 2 an explicit expression for a useful character sum associated with the symmetric group 4 contains a number of results for symmetric functions that are equivalent to theorem 2 1 these include a generalization of cauchy s summation theorem for

infinite non simple c algebras absorbing the cuntz algebra o abstract the first named author has given a classification of all separable nuclear c algebras a that absorb the cuntz algebra o we say that a absorbs o if a is isomorphic to a o motivated by this classification we investigate here if one can give an intrinsic characterization of c algebras that absorb o this investigation leads us to three different notions of pure infiniteness of a c algebra all given in terms of local algebraic conditions on the c algebra the strongest of the three properties strongly purely infinite is shown to be equivalent to absorbing o for separable nuclear c algebras that either are stable or have an approximate unit consisting of projections in a previous paper 2000 amer j math 122 637 666 we studied an intermediate and perhaps more natural condition purely infinite that extends a well known property for simple c algebras the weakest condition of the three weakly purely infinite is shown to be equivalent to the absence of quasitraces in an ultrapower of the c algebra the three conditions may be equivalent for all c algebras and we prove this to be the case for c algebras that are either simple of real rank zero or approximately divisible

bishop phelps bollobas property for certain spaces of operators abstract we characterize the banach spaces y for which certain subspaces of operators from l 1 into y have the bishop phelps bollobas property in terms of a geometric property of y namely ahsp this characterization applies to the spaces of compact and weakly compact operators new examples of banach spaces y with ahsp are provided we also obtain that certain ideals of asplund operators satisfy the bishop phelps bollobas property

lushness numerical index one and duality we construct an example of a banach space which is not lush but whose dual space is lush this example shows that lushness is not equivalent to numerical index one a characterization of lushness for some quotient spaces of l1 spaces and new results on c rich subspaces of scalar or vector valued c k spaces are also presented

purely infinite crossed products by endomorphisms 2013 elsevier inc all rights reserved this is the authors accepted and refereed manuscript to the article author s post print must be released with a creative commons attribution non commercial no derivatives license

pure infiniteness and ideal structure of c algebras associated to fell bundles abstract we investigate structural properties of the reduced cross sectional algebra c r b of a fell bundle b over a discrete group g conditions allowing one to determine the ideal structure of c r b are studied notions of aperiodicity paradoxicality and b infiniteness for the fell bundle b are introduced and investigated by themselves and in relation to the partial dynamical system dual to b several criteria of pure infiniteness of c r b are given it is shown that they generalize and unify corresponding results obtained in the context of crossed products by the following duos laca spielberg 34 jolissaint robertson 21 sierakowski rordam 47 giordano sierakowski 18 and ortega pardo 39 for exact separable fell bundles satisfying the residual intersection property primitive ideal space of c r b is determined the results of the paper are shown to be optimal when applied to graph c algebras applications to a class of exel larsen crossed products are presented

co universal algebras associated to product systems and gauge invariant uniqueness theorems let x be a product system over a quasi lattice ordered group under mild hypotheses we associate to x a c algebra which is co universal for injective nica covariant toeplitz representations of x which preserve the gauge coaction under appropriate amenability criteria this co universalc algebra coincides with the cuntz nica pimsner algebra introduced by sims and yeend we prove two key uniqueness theorems and indicate how to use our theorems to realise a number of reduced crossed products as instances of our co universal algebras in each case it is an easy corollary that the cuntz nica pimsner algebra is isomorphic to the corresponding full crossed product

a characterization of the schur property through the disk algebra abstract in this paper we give a new characterization of when a banach space e has the schur property in terms of the disk algebra we prove that e has the schur property if and only if a d e a d e w

some geometric properties of disk algebras abstract in this paper we study some geometrical properties of certain classes of uniform algebras in particular the ball algebra a u b x of all uniformly continuous functions on the closed unit ball and holomorphic on the open unit ball of a complex banach space x we prove that a u b x has k numerical index 1 for every k the lushness and also the ahsp moreover the disk algebra a d and more in general any uniform algebra whose choquet boundary has no isolated points is proved to have the polynomial daugavet property most of those properties are extended to the vector valued version a x of a uniform algebra a

on the morita equivalence of tensor algebras our objective is two fold first we want to develop a notion of morita equivalence for c correspondences that guarantees that if two c correspondences e and f are morita equivalent then the tensor algebras of e and f taoeu and taofu are strongly morita equivalent in the sense of 8 the toeplitz algebras toeu and tofu are strongly morita equivalent in the sense of rieffel 32 see 33 also and the cuntz pimsner algebras 28 ooeu and oofu are strongly morita equivalent in the same sense we were inspired by earlier work of curto williams and the first author in 15 and combes 14 these papers investigate conditions implying that the crossed product of two c dynamical systems are strongly morita equivalent given that the coefficient algebras are strongly morita equivalent abadie eilers and exel 1 were similarly inspired and developed a theory of morita equivalence for special c correspondences our analysis extends theirs but our arguments are different see example 2 5 and remarks 3 3 and 3 6 for a comparison of their results and ours second we want to investigate the converse implication that is we study the following question if taoeu and taofu are strongly morita equivalent in the sense of 8 when are e and f morita equivalent in the sense we define for this converse direction we focus on the tensor algebras rather than the toeplitz and cuntz pimsner algebras because very little can be said in the self adjoint setting here we were inspired by arveson s paper 2 in which it is proved that two ergodic measure preserving transformations are conjugate if and only if certain non self adjoint crossed products associated with the transformations are algebraically isomorphic see 3 also his analysis was further extended by k saito and the first author to cover non self adjoint crossed products built from automorphisms of general von neumann algebras they showed that non self adjoint crossed products built from properly outer automorphisms of von neumann algebras are isomorphic if and only if the automorphisms are conjugate see 22 and 23 our principal result in the converse direction theorem 7 2 asserts that if e and f are two aperiodic correspondences and if taoeu is strongly morita equivalent to taofu in the sense of 8 then e and f are morita equivalent as we shall see in 5 the notion of aperiodicity is an exact analogue for correspondences of the concept of free action in ergodic theory free action was a central hypothesis in arveson s

the bishop phelps bollobas property and lush spaces abstract we prove that for every lush space x the couple l 1 x has the bishop phelps bollobas property for operators that is every lush space has the ahsp standing for the approximate hyperplane series property while every lush space has the alternative daugavet property there exists a space with the alternative daugavet property that does not have the ahsp we also show that there is a banach space with both the ahsp and the alternative daugavet property which is not lush

topological aperiodicity for product systems over semigroups of ore type we prove a version of uniqueness theorem for cuntz pimsner algebras of discrete product systems over semigroups of ore type to this end we introduce doplicher roberts picture of cuntz pimsner algebras and the semigroup dual to a product system of regular c correspondences under a certain aperiodicity condition on the latter we obtain the uniqueness theorem and a simplicity criterion for the algebras in question these results generalize the corresponding ones for crossed products by discrete groups due to archbold and spielberg and for exel s crossed products due to exel and vershik they also give interesting conditions for topological higher rank graphs and p graphs and apply to the new cuntz c algebra qn arising from the ax b semigroup over n

crossed products by spectrally free actions abstract we define spectral freeness for actions of discrete groups on c algebras we relate spectral freeness to other freeness conditions an example result is that for an action of a finite group g spectral freeness is equivalent to strong pointwise outerness and also to the condition that g 1 for every g g 1 we then prove permanence results for reduced crossed products by exact spectrally free actions for crossed products by arbitrary actions of z 2 z and for extensions direct limits stable isomorphism and several related constructions for the following properties the combination of pure infiniteness and the ideal property residual hereditary infiniteness closely related to pure infiniteness residual sp a strengthening of property sp suitable for nonsimple c algebras the weak ideal property closely related to the ideal property for the weak ideal property we can allow arbitrary crossed products by any finite abelian group these properties of c algebras are shown to have formulations of the same general type allowing them all to be handled using a common set of theorems

banach spaces with the daugavet property a banach space x is said to have the daugavet property if every operator t x x of rank 1 satisfies 11 id tl 1 fltil we show that then every weakly compact operator satisfies this equation as well and that x contains a copy of t1 however x need not contain a copy of l1 we also study pairs of spaces x c y and operators t x y satisfying i i j t i i 1 4 1f t i i where j x y is the natural embedding this leads to the result that a banach space with the daugavet property does not embed into a space with an unconditional basis in another direction we investigate spaces where the set of operators with f id tll 1 il t l i is as small as possible and give characterisations in terms of a smoothness condition