Related papers: Introduction to Normed *-Algebras and their Repres…

In this paper, we introduce a C*-algebra associated to any substitution (via its Bratteli diagram model). We show that this C*-algebra contains the partial crossed product C*-algebra of the corresponding Bratteli-Vershik system and show…

We prove that unital surjective spectral isometries on certain non-simple unital C*-algebras are Jordan isomorphisms. Along the way, we establish several general facts in the setting of semisimple Banach algebras.

Blecher and Read have recently introduced and studied a new notion of positivity in operator algebras, with an eye to extending certain $C^*$-algebraic results and theories to more general algebras. In the present paper we generalize some…

We study some general properties of tracial C*-algebras. In the first part, we consider Dixmier type approximation theorem and characterize symmetric amenability for C*-algebras. In the second part, we consider continuous bundles of tracial…

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…

We compare and classify various types of Banach algebra norms on mathbb{C}^k through geometric properties of their unit balls. This study is motivated by various open problems in interpolation theory and in the isometric characterization of…

Given a connected and locally compact Hausdorff space X with a good base K we assign, in a functorial way, a C(X)-algebra to any precosheaf of C*-algebras A defined over K. Afterwards we consider the representation theory and the Kasparov…

We start with definitions of the general notions of the theory of $\Bbb Z_{2}$-graded algebras. Then we consider theory of inductive families of $\Bbb Z_{2}$-graded semisimple finite-dimensional algebras and its representations in the…

It is shown that all the approximately finite dimensional C*-algebras which are not of Type I are isomorphic as Banach spaces. This generalises the matroid case given previously by Arazy. Analogous results are obtained for various families…

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…

In this note, we show that the spectral theorem, has two representations; the Stone-von Neumann representation and one based on the polar decomposition of linear operators, which we call the deformed representation. The deformed…

We begin the systematic model theoretic study of $\mathrm{C}^*$-algebras using the tools of continuous logic.

In this dissertation we study the category of completely positive normal contractive maps between von Neumann algebras. It includes an extensive introduction to the basic theory of $C^*$-algebras and von Neumann algebras.

This article is an expository account of the theory of twisted commutative algebras, which simply put, can be thought of as a theory for handling commutative algebras with large groups of linear symmetries. Examples include the coordinate…

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…

In this note we analyze the C*-algebra associated with a branched covering both as a groupoid C*-algebra and as a Cuntz-Pimsner algebra. We determine conditions when the algebra is simple and purely infinite. We indicate how to compute the…

This is a survey paper about representation theory and noncommutative geometry of reductive p-adic groups G. The main focus points are: 1. The structure of the Hecke algebra H(G), the Harish-Chandra-Schwartz algebra S(G) and the reduced…

We consider a class of C*-algebras C(X) associated with quantum spaces such as spheres, projective spaces, and lens spaces. We introduce a non-self-adjoint operator algebra A together with an explicit functor from the category of…

We introduce Banach algebras associated to twisted \'etale groupoids $(\mathcal{G},\mathcal{L})$ and to twisted inverse semigroup actions. This provides a unifying framework for numerous recent papers on $L^p$-operator algebras and the…

We describe the main algebraic and geometric properties of the class of algebras introduced in [arXiv:0705.1629]. We discuss their origins in symplectic geometry and associative algebra, and the notions of cohomology and representations. We…