Related papers: Hilbert C*-modules over a commutative C*-algebra

We introduce the $B$-spline interpolation problem corresponding to a $C^*$-valued sesquilinear form on a Hilbert $C^*$-module and study its basic properties as well as the uniqueness of solution. We first study the problem in the case when…

This paper addresses the problem of describing the structure of tensor C*-categories M with conjugates and irreducible tensor unit. No assumption on the existence of a braided symmetry or on amenability is made. Our assumptions are…

Cuntz and Li have defined a C*-algebra associated to any integral domain, using generators and relations, and proved that it is simple and purely infinite and that it is stably isomorphic to a crossed product of a commutative C*-algebra. We…

The cone of lower semicontinuous traces is studied with a view to its use as an invariant. Its properties include compactness, Hausdorffness, and continuity with respect to inductive limits. A suitable notion of dual cone is given. The cone…

We find first structural background information about the reasons that for any C*-algebra $A$ and any two Hilbert $A$-modules $M \subseteq N$ with $M^\perp=\{0\}$, every bounded $A$-linear map $N \to A$ (or $N \to N)$ vanishing on $M$ might…

In this article, we study tensor product of Hilbert $C^*$-modules and Hilbert spaces. We show that if $E$ is a Hilbert $A$-module and $F$ is a Hilbert $B$-module, then tensor product of frames (orthonormal bases) for $E$ and $F$ produce…

We initiate a study of Hilbert modules over the polynomial algebra A=C[z_1,...,z_d] that are obtained by completing A with respect to an inner product having certain natural properties. A standard Hilbert module is a finite multiplicity…

Given a compact, metric space X, we show that the commutative C*-algebra C(X) is semiprojective if and only if X is an absolute neighborhood retract of dimension at most one. This confirms a conjecture of Blackadar. Generalizing to the…

We develop a theory of Hilbert $\widetilde{\C}$-modules by investigating their structural and functional analytic properties. Particular attention is given to finitely generated submodules, projection operators, representation theorems for…

Let $H$ be a separable Hilbert space with a fixed orthonormal basis. Let $\mathbb B^{(k)}(H)$ denote the set of operators, whose matrices have no more than $k$ non-zero entries in each line and in each column. The closure of the union (over…

Suppose a C*-algebra A acts by adjointable operators on a Hilbert A-module X. Pimsner constructed a C*-algebra O_X which includes, for particular choices of X, crossed products of A by Z, the Cuntz algebras O_n, and the Cuntz-Krieger…

We revisit the characterisation of modules over non-unital $C^*$-algebras analogous to modules of sections of vector bundles. A fullness condition on the associated multiplier module characterises a class of modules which closely mirror the…

This is a graduate-level introduction to C*-algebras, Hilbert C*-modules, vector bundles, and induced representations of groups and C*-algebras, with applications to quantization theory, phase space localization, and configuration space…

In previous work, we defined and studied $\Sigma^*$-modules, a class of Hilbert $C^*$-modules over $\Sigma^*$-algebras (the latter are $C^*$-algebras that are sequentially closed in the weak operator topology). The present work continues…

In Rev. Math. Phys. 4 (1997) 785 we study Hilbert-C* systems {F,G} where the fixed point algebra A has nontrivial center Z and where A'\cap F=Z is satisfied. The corresponding category of all canonical endomorphisms of A contains…

Given a compact metric space X and a unital C*-algebra A, we introduce a family of seminorms on the C*-algebra of continuous functions from X to A, denoted C(X, A), induced by classical Lipschitz seminorms that produce compact quantum…

This paper continues the study of holomorphic semistable principal G-bundles over an elliptic curve. In this paper, the moduli space of all such bundles is constructed by considering deformations of a minimally unstable G-bundle. The set of…

The overview contains 450 references of books, chapters of monographs, papers, preprints and Ph.~D.~thesises which are concerned with the theory and/or various applications of Hilbert C*-modules. To show a way through this amount of…

We give a new Banach module characterization of $W^*$-modules, also known as selfdual Hilbert $C^*$-modules over a von Neumann algebra. This leads to a generalization of the notion, and the theory, of W*-modules, to the setting where the…

We single out the concept of concrete Hilbert module over a locally $C^*$-algebra by means of locally bounded operators on certain strictly inductive limits of Hilbert spaces. Using this concept, we construct an operator model for all…