Related papers: Homomorphic conditional expectations as noncommuta…

We show that a $C^*$-algebra $\mathfrak{A}$ which is stably isomorphic to a unital graph $C^*$-algebra, is isomorphic to a graph $C^*$-algebra if and only if it admits an approximate unit of projections. As a consequence, a hereditary…

We study properties of C*-algebraic deformations of homogeneous spaces $G/\Gamma$ which are equivariant in the sense that they preserve the natural action of $G$ by left translation. The center is shown to be isomorphic to $C(G/G_\rho^0)$…

The canonical trace on the reduced C*-algebra of a discrete group gives rise to a homomorphism from the K-theory of this C^*-algebra to the real numbers. This paper addresses the range of this homomorphism. For torsion free groups, the…

Let $\gamma = (\gamma_1,...,\gamma_N)$, $N \geq 2$, be a system of proper contractions on a complete metric space. Then there exists a unique self-similar non-empty compact subset $K$. We consider the union ${\mathcal G} = \cup_{i=1}^N…

We introduce a class of good endofunctors of $C^{*}$-algebras, endow it with a structure of a bimonoidal category, and define homotopies of natural transformations between such endofunctors. For every pair of $C^{*}$-algebras and a good…

Let $K$ be a field of characteristic $0$ and let $G$ and $H$ be connected commutative algebraic groups over $K$. Let $\text{Mor}_0(G,H)$ denote the set of morphisms of algebraic varieties $G \to H$ that map the neutral element to the…

Let K be any compact set. The C^*-algebra C(K) is nuclear and any bounded homomorphism from C(K) into B(H), the algebra of all bounded operators on some Hilbert space H, is automatically completely bounded. We prove extensions of these…

This paper addresses the isomorphism problem for the universal (nonself-adjoint) operator algebras generated by a row contraction subject to homogeneous polynomial relations. We find that two such algebras are isometrically isomorphic if…

Every homomorphism $\varphi: B(G) \rightarrow B(H)$ between Fourier-Stieltjes algebras on locally compact groups $G$ and $H$ is determined by a continuous mapping $\alpha: Y \rightarrow \Delta(B(G))$, where $Y$ is a set in the open coset…

Conic quasi-linear maps are nonlinear operators from $C_0(X)$ to a normed linear space $E$ which preserve nonnegative linear combinations on positive cones generated by single functions; quasi-linear maps are linear on singly generated…

We classify unital monomorphisms into certain simple Z-stable C^*-algebras up to approximate unitary equivalence. The domain algebra C is allowed to be any unital separable commutative C^*-algebra, or any unital simple separable nuclear…

For a given extension $A \subset E$ of associative algebras we describe and classify up to an isomorphism all $A$-complements of $E$, i.e. all subalgebras $X$ of $E$ such that $E = A + X$ and $A \cap X = \{0\}$. Let $X$ be a given…

Given an arbitrary countable ordinal $\alpha $, we introduce the notion of type $I_{\alpha }$ C*-algebra and $\alpha $-subhomogeneous C*-algebra. When $\alpha =0$, these recover the notions of Fell C*-algebra and of commutative C*-algebra,…

Attractor-repeller decompositions of isolated invariant sets give rise to so-called connecting homomorphisms. These homomorphisms reveal information on the existence and structure of connecting trajectories of the underlying dynamical…

What is the correct noncommutative generalization of the functor $C_0(X) \mapsto \ell^\infty(X)$ for locally compact Hausdorff $X$ having a countable basis? Making the ansatz $K(\ell^2) \mapsto B(\ell^2)$, we expect that every unital…

Let $R$ be a root datum with affine Weyl group $W^e$, and let $H = H (R,q)$ be an affine Hecke algebra with positive, possibly unequal, parameters $q$. Then $H$ is a deformation of the group algebra $\mathbb C [W^e]$, so it is natural to…

Let A be a C*-algebra and d from A into A** be a continuous linear map. We assume that d acts like derivation or anti-derivation at orthogonal elements for several types of orthogonality conditions such as ab=0, ab*=0, ab=ba=0 and…

Let Map(K,X) denote the space of pointed continuous maps from a finite cell complex K to a space X. Let E_* be a generalized homology theory. We use Goodwillie calculus methods to prove that under suitable conditions on K and X, Map(K, X)…

The paper presents a criterion for a C*-algebra to be a coefficient algebra associated with a given endomorphism

We introduce and characterize a particularly tractable class of unital type 1 C*-algebras with bounded dimension of irreducible representations. Algebras in this class are called recursive subhomogeneous algebras, and they have an inductive…