Related papers: Morphisms of certain Banach C*-modules

In this project, we will develop the theory of Banach algebras and prove two celebrated theorems, the Gelfand representation theorem and the GKZ theorem. We will then proceed to develop the theory of $C^*$-algebras and prove the…

The following topics are presented in these notes: Elements of Banach algebras, Banach algebras of the form $L^1(G)$, where $G$ is a locally compact group, spectrum of elements of Banach algebras, the spectral theory of compact operators on…

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.

We introduce the notion of a (noncommutative) C*-Segal algebra as a Banach algebra which is a dense ideal in a C*-algebra. Several basic properties are investigated and, with the aid of the theory of multiplier modules, the structure of…

Non-commutative $L^p$-spaces are shown to constitute examples of a class of Banach quasi *-algebras called CQ*-algebras. For $p\geq 2$ they are also proved to possess a {\em sufficient} family of bounded positive sesquilinear forms…

This book treats: - spectral theory of Banach *-algebras, - basic representation theory of normed *-algebras, - spectral theory of representations of commutative *-algebras. A novel feature of the book is the construction of the enveloping…

This book treats: - spectral theory of Banach *-algebras, - basic representation theory of normed *-algebras, - spectral theory of representations of commutative *-algebras. A novel feature of the book is the construction of the enveloping…

The GNS construction for positive invariant sesquilinear forms on quasi *-algebras is generalized to a class of positive C*-valued sesquilinear maps on quasi *-algebras. The result is a *-representation taking values in a space of operators…

The approach we present is a modification of the Morse theory for unital C*-algebras. We provide tools for the geometric interpretation of noncommutative CW complexes. These objects were introduced and studied in [2],[7] and [14]. Some…

Geometric realizations for the restrictions of GNS representations to unitary groups of $C^*$-algebras are constructed. These geometric realizations use an appropriate concept of reproducing kernels on vector bundles. To build such…

We show three Hahn-Banach type extension criteria for (sets of) bounded C*-linear maps of Hilbert C*-modules to the underlying C*-algebras of coefficients. One criterion establishes an alternative description of the property of (AW*-)…

This book treats: - spectral theory of Banach *-algebras, - basic representation theory of normed *-algebras, - spectral theory of representations of commutative *-algebras. A novel feature of the book is the construction of the enveloping…

We introduce C*-algebras over C_{\infty}(Q,C) as Banach-Kantorovich *-algebras over the algebra C_{\infty}(Q,C) of extended continuous complex-valued functions, defined on comeager subsets of Stonean compact Q, whose norm satisfies…

A Hilbert $C^*$-quad module of finite type has a multi structure of Hilbert $C^*$-bimodules with two finite bases. We will construct a $C^*$-algebra from a Hilbert $C^*$-quad module of finite type and prove its universality subject to…

Reduced HNN extensions of von Neumann algebras (as well as $C^*$-algebras) will be introduced, and their modular theory, factoriality and ultraproducts will be discussed. In several concrete settings, detailed analysis on them will be also…

We introduce a notion of Krein C*-module over a C*-algebra and more generally over a Krein C*-algebra. Some properties of Krein C*-modules and their categories are investigated.

Properties of the inverse along an element in rings with an involution, Banach algebras and $C^*$-alegbras will be studied unifying known expressions concerning generalized inverses.

Let G be a locally compact group and rho a non-unitary finite dimensional representation of G. We consider tensor products of rho by some unitary representations of G in order to define two Banach algebras analogous to the group…

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 we study the structure of the $C^*$-algebra, generated by the representation of the paths semigroup on a partially ordered set (poset) and get the net of isomorphic $C^*$-algebras over this poset. We construct the extensions…