Related papers: Lectures on C*-algebras

Further to the functional representations of C$^*$-algebras proposed by R. Cirelli, A. Mania and L. Pizzocchero, we consider in this article the uniform K\"ahler bundle (in short, UKB) description of some C$^*$-algebraic subjects. In…

In this paper, we introduce the notion of invariant submodule in the theory of Hilbert C*-modules and study some basic properties of bounded adjointable operators and their generalized inverses which have nontrivial invariant submodules. We…

For a compact Hausdorff space $X$, the space $SC(X\times X)$ of separately continuous complex valued functions on $X$ can be viewed as a $C^*$-subalgebra of $C(X)^{**}\overline\otimes C(X)^{**}$, namely those elements which slice into…

Let $\ell$ be a length function on a group $G$, and let $M_{\ell}$ denote the operator of pointwise multiplication by $\ell$ on $\bell^2(G)$. Following Connes, $M_{\ell}$ can be used as a ``Dirac'' operator for $C_r^*(G)$. It defines a…

Let G be a locally compact group, M(G) denote its measure algebra and L^1(G) denote its group algebra. Also, let pi:G->U(H) be a strongly continuous unitary representation, and let CB^{sigma}(B(H)) be the space of normal completely bounded…

We define a categorical framework in which we build a systematic construction that provides generic invariants for C*-algebras. The benefit is significant as we show that any invariant arising this way automatically enjoys nice properties…

We introduce the notion of envelope of a topological algebra (in particular, an arbitrary associative algebra) with respect to a class of Banach algebras. In the case of the class of real Banach algebras of polynomial growth, i.e.,…

The notion of bounded element of C*-inductive locally convex spaces (or C*-inductive partial *-algebras) is introduced and discussed in two ways: the first one takes into account the inductive structure provided by certain families of…

Categories of paths are a generalization of several kinds of oriented discrete data that have been used to construct $C^*$-algebras. The techniques introduced to study these constructions apply almost verbatim to the more general situation…

We study the closed algebra B_I(G) generated by the idempotents in the Fourier-Stieltjes algebra of a locally compact group G. We show that it is a regular Banach algebra with computable spectrum G^I, which we call the idempotent…

Let $G$ be a locally compact, compactly generated group of polynomial growth and let $\omega$ be a weight on $G$. Under proper assumptions on the weight $\omega$, the Banach space $L^p(G,\omega)$ is a Banach \ast-algebra. In this paper we…

Motivated by the beautiful work of M. A. Rieffel (1965) and of M. E. Walter (1974), we obtain characterisations of the Fourier algebra $A(G)$ of a locally compact group $G$ in terms of the class of $F$-algebras (i.e. a Banach algebra $A$…

We prove that the C*-algebra of a minimal diffeomorphism satisfies Blackadar's Fundamental Comparability Property for positive elements. This leads to the classification, in terms of K-theory and traces, of the isomorphism classes of…

The article is devoted to investigation of classes of functions monotone as functions on general $C^*$-algebras that are not necessarily the $C^*$-algebras of all bounded linear operators on a Hilbert space as it is in classical case of…

We explore the recently introduced local-triviality dimensions by studying gauge actions on graph $C^*$-algebras, as well as the restrictions of the gauge action to finite cyclic subgroups. For $C^*$-algebras of finite acyclic graphs and…

We define and study the notion of property $(\rm T)$ for Banach algebras, generalizing the one from $C^*$-algebras. For a second countable locally compact group $G$ and a given family of Banach spaces $\mathcal E$, we prove that our Banach…

To each unital C*-algebra A we associate a presheaf \Sigma^A, called the spectral presheaf of A, which can be regarded as a generalised Gelfand spectrum. We develop a categorical notion of local duality and show that there is a…

The construction of the C*-algebra associated to a directed graph $E$ is extended to incorporate a family $C$ consisting of partitions of the sets of edges emanating from the vertices of $E$. These C*-algebras $C^*(E,C)$ are analyzed in…

Let $L$ be a length function on a group $G$, and let $M_L$ denote the operator of pointwise multiplication by $L$ on $\ell^2(G)$. Following Connes, $M_L$ can be used as a "Dirac" operator for the reduced group C*-algebra $C_r^*(G)$. It…

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…