Related papers: Locally inner automorphisms of operator algebras

We obtain two characterizations of the bi-inner Hopf *-automorphisms of a finite-dimensional Hopf C*-algebra, by means of an analysis of the structure of convolution products in this class of Hopf C*-algebra.

The $2$-adic ring $C^*$-algebra $\mathcal{Q}_2$ naturally contains a copy of the Cuntz algebra $\mathcal{O}_2$ and, a fortiori, also of its diagonal subalgebra $\mathcal{D}_2$ with Cantor spectrum. This paper is aimed at studying the group…

We show that any order isomorphism between ordered structures of associative unital JB-subalgebras of JBW algebras is implemented naturally by a Jordan isomorphism. Consequently, JBW algebras are determined by the structure of their…

We obtain a description of the C*-algebras which can occur as a simple quotient of the C*-algebra of a locally injective surjection on a compact metric space of finite covering dimension.

Investigating the direct integral decomposition of von Neumann algebras of bounded module operators on self-dual Hilbert W*-moduli an equivalence principle is obtained which connects the theory of direct disintegration of von Neumann…

We characterize the canonical diagonal subalgebra of the C*-algebra associated with a generalized Boolean dynamical system. We also introduce a particular commutative subalgebra, which we call the abelian core, in our C*-algebra. We then…

We revisit a well-known "surjectivity onto quotient" type lemma of Kirchberg on the central sequence algebra of a separable unital ${\rm C}^*$-algebra, and use it to prove a "surjectivity onto quotient" result on approximately inner…

We obtain partial affirmative answers to the question whether isomorphism of the unitary groups of two C*-algebras, either as topological groups or as discrete groups, implies isomorphism of the C*-algebras as real C*-algebras.

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…

When $\mathcal D$ is strongly self-absorbing we say an inclusion $B \subseteq A$ is $\mathcal D$-stable if it is isomorphic to the inclusion $B \otimes \mathcal D \subseteq A \otimes \mathcal D$. We give ultrapower characterizations and…

In the paper, we give two new characterizations of separable inner quasidiagonal C*-algebras. Base on these characterizations, we show that a unital full free product of two inner quasidiagonal C*-algebras is inner quasidiagonal again. As…

We construct the full and reduced C*-algebras of an ample groupoid from its complex Steinberg algebra. We also show that our construction gives the same C*-algebras as the standard constructions. In the last section, we consider an…

We prove automatic continuity theorems for "decomposable" or "local" linear transformations between certain natural subspaces of operator algebras. The transformations involved are not algebra homomorphisms but often are module…

We prove a new uniqueness theorem for the tight C*-algebras of an inverse semigroup by generalizing the uniqueness theorem given for \'etale groupoid C*-algebras by Brown, Nagy, Reznikoff, Sims, and Williams. We use this to show that in the…

The aim of this note is to show that the automorphism and isometry groups of the C*-algebra $\l_\infty(N,B(H))$ of all bounded sequences in $B(H)$ are topologically reflexive which, as one of our former results shows, is not the case with…

It is well known that every derivation of a von Neumann algebra into itself is an inner derivation and that every derivation of a von Neumann algebra into its predual is inner. It is less well known that every triple derivation (defined…

We prove that the pure state space is homogeneous under the action of the automorphism group (or a certain smaller group of approximately inner automorphisms) for a fairly large class of simple separable nuclear C*-algebras, including the…

Many important quantum algebras such as quantum symplectic space, quantum Euclidean space, quantum matrices, $q$-analogs of the Heisenberg algebra and the quantum Weyl algebra are semi-commutative. In addition, enveloping algebras $U(L_+)$…

We study the elementary C*-algebra whose elements are the sum of a diagonal plus a compact operator. We describe the structure of the unitary group, the sets of ideals, automorhisms and projections.

In this paper we give some characterizations of M. Hamana's injective envelope I(A) of a C*-algebra A in the setting of operator spaces and completely bounded maps. These characterizations lead to simplifications and generalizations of some…