Related papers: $C^{*}$-algebras isomorphically representable on $…

We say that a $C^*$-algebra $\mathcal{A}$ satisfies the similarity property ((SP)) if every bounded homomorphism $u\colon \mathcal{A} \to \mathcal{B}(\mathit{H})$, where $\mathit{H}$ is a Hilbert space, is similar to a $*$-homomorphism. We…

Let $p\in(1,\infty)$. We show that there is an isomorphism from any separable unital subalgebra of $B(\ell^{2})/K(\ell^{2})$ onto a subalgebra of $B(\ell^{p})/K(\ell^{p})$ that preserves the Fredholm index. As a consequence, every separable…

We show that with few exceptions every local isometric automorphism of the group algebra $L^p(G)$ of a compact group $G$ is an isometric automorphism.

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…

It is shown that every linear strong Birkhoff-James isomorphism between unital $C^*$-algebras is a $*$-isomorphism followed by a unitary multiplication. Moreover, as a partial extension of this result to the non-unital case, the form of…

For $p\in [1,\infty)$, we show that every unital $L^p$-operator algebra contains a unique maximal $C^*$-subalgebra, which is always abelian if $p\neq 2$. Using this, we canonically associate to every unital $L^p$-operator algebra $A$ an…

Every separable nondegenerate C*-correspondence over a commutative C*-algebra with discrete spectrum is isomorphic to a graph correspondence.

We describe proper correspondences from graph C*-algebras to arbitrary C*-algebras by K-theoretic data. If the target C*-algebra is a graph C*-algebra as well, we may lift an isomorphism on a certain invariant to correspondences back and…

A C*-algebra is n-homogeneous (where n is finite) if every its nonzero irreducible representation acts on an n-dimensional Hilbert space. An elementary proof of Fell's characterization of n-homogeneous C*-algebras (by means of their…

Let $A$ be a $C^*$-algebra. We say that $A$ satisfies the SP if every bounded homomorphism $A\to B(K)$, with $K$ a Hilbert space, is similar to a $*$-homomorphism. We introduce three hypotheses that relate to extending hyperreflexive…

We show that a representation of a Banach algebra $A$ on a Banach space $X$ can be extended to a canonical representation of $A^{**}$ on $X$ if and only if certain orbit maps $A\to X$ are weakly compact. When this is the case, we show that…

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…

We introduce the concept of finitely coloured equivalence for unital *-homomorphisms between C*-algebras, for which unitary equivalence is the 1-coloured case. We use this notion to classify *-homomorphisms from separable, unital, nuclear…

We prove some stability results for certain classes of C*-algebras. We prove that whenever $A$ is a finite-dimensional C*-algebra, $B$ is a C*-algebra and $\phi\colon A\to B$ is approximately a $^*$-homomorphism then there is an actual…

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 give a sufficient condition for a $^*$-algebra with a specified basis to have an enveloping $C^*$-algebra. Particularizing to the setting of a Hecke algebra $\h(G,\gm)$, we show that under a suitable assumption not only we can assure…

In this paper, we prove that unital homomorphisms from continuous functions on a compact metric space to matrices over a C*-algebra with tracial rank at most one are approximately diagonalizable. We also consider some generalizations of…

We survey the results on linear local and 2-local homomorphisms and zero products preserving operators between C$^*$-algebras, and we incorporate some new precise observations and results to prove that every bounded linear 2-local…

We consider the functor C that to a unital C*-algebra A assigns the partial order set C(A) of its commutative C*-subalgebras ordered by inclusion. We investigate how some C*-algebraic properties translate under the action of C to…

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.