Related papers: Hilbert modules over locally C*-algebras

We study the theory of a Hilbert space H as a module for a unital C*-algebra A from the point of view of continuous logic. We give an explicit axiomatization for this theory and describe the structure of all the representations which are…

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…

In this paper, by analogy with the case of C*-algebras, we define the notion of induced representation of a locally C*-algebra, and then we prove a imprimitivity theorem for induced representations of locally C*-algebras.

A Hilbert module is a generalisation of a Hilbert space for which the inner product takes its values in a C*-algebra instead of the complex numbers. We use the bracket product to construct some Hilbert modules over a group C*-algebra which…

We study representations of Hilbert bimodules on pairs of Hilbert spaces. If $A$ is a C*-algebra and $\mathsf{X}$ is a right Hilbert $A$-module, we use such representations to faithfully represent the C*-algebras $\mathcal{K}_A(\mathsf{X})$…

We introduce a method to define $C^*$-algebras from $C^*$-correspondences. Our construction generalizes Cuntz-Pimsner algebras, crossed products by Hilbert $C^*$-modules, and graph algebras.

A precise description of the injective envelope of a spatial continuous trace C*-algebra A over a Stonean space Delta is given. The description is based on the notion of a weakly continuous Hilbert bundle, which we show to be a…

Let H be a full Hilbert bimodule over a C*-algebra A. We show that the Cuntz-Pimsner C*-algebra associated to H is exact if and only if A is exact. Using this result, we give alternative proofs for exactness of reduced amalgamated free…

Let $A$ and $B$ be arbitrary $C^*$-algebras, we prove that the existence of a Hilbert $A$-$B$-bimodule of finite index ensures that the WEP, QWEP, and LLP along with other finite-dimensional approximation properties such as CBAP and (S)OAP…

We introduce $C^*$-pseudo-multiplicative unitaries and (concrete) Hopf $C^*$-bimodules, which are $C^*$-algebraic variants of the pseudo-multiplicative unitaries on Hilbert spaces and the Hopf-von Neumann-bimodules studied by Enock,…

It is shown that if A is a stably finite C*-algebra and E is a countably generated Hilbert A-module, then E gives rise to a compact element of the Cuntz semigroup if and only if E is algebraically finitely generated and projective. It…

This paper explores the concept of $K$-$g$-frames in locally $C^*$-algebras, which are shown to be more general than $g$-frames. The authors first introduce the notion of a $g$-orthonormal basis and utilize it to define the $g$-operator, a…

We study left-invariant locally conformally K\"ahler structures on Lie groups, or equivalently, on Lie algebras. We give some properties of these structures in general, and then we consider the special cases when its complex structure is…

Let F be a right Hilbert C*-module over a C*-algebra B, and suppose that F is equipped with a left action, by compact operators, of a second C*-algebra A. Tensor product with F gives a functor from Hilbert C*-modules over A to Hilbert…

We define the localisation of a Hilbert module in analogy to the local multiplier algebra. We use properties of this localisation to enrich non-closed actions on $C^*$-algebras to closed actions on local multiplier algebras, and descend…

We introduce and study locally AW*-algebras (Baer locally C*-algebras) as a locally multiplicatively-convex generalization of AW*-algebras of Kaplansky. Among other basic properties of these algebras, it is established that: {\bullet} A…

Let $A$ be a simple C*-algebra of stable rank one and let $p$ and $q$ be two $\sigma$-compact open projections. It is proved that there is a continuous path of unitaries in ${\tilde A}$ which connects open sub-projections of $p$ which is…

Given a skeletally small category $\mathcal{C}$, we show that any locally finite endo-length $\mathcal{C}$-module is the direct sum of indecomposable $\mathcal{C}$-modules, whose endomorphism algebra is local.

In this paper, we investigate some characterizations of dual continuous frames and give some results about them. Also, we refer to the method of constructing a family of duals through a fixed dual and show there exists a one-to-one…

This work provides a generalization of the Gelfand duality to the context of noncommutative locally $C^*$ algebras. Using a reformulation of a theorem proven by Dauns and Hofmann in the 60's we show that every locally $C^*$ algebra can be…