Related papers: When is Every Quasi-Multiplier a Multiplier?

We consider the question of when the multiplier algebra $M(\mathcal{A})$ of a $C^*$-algebra $\mathcal{A}$ is a $ W^*$-algebra, and show that it holds for a stable $C^*$-algebra exactly when it is a $C^*$-algebra of compact operators. This…

A $\Sigma^*$-algebra is a concrete $C^*$-algebra that is sequentially closed in the weak operator topology. We study an appropriate class of $C^*$-modules over $\Sigma^*$-algebras analogous to the class of $W^*$-modules (selfdual…

We discuss necessary as well as sufficient conditions for the second iterated local multiplier algebra of a separable C*-algebra to agree with the first.

If $A$ is a $\sigma$-unital $C^*$-algebra and $a$ is a strictly positive element of $A$ then for every compact subset $K$ of the complete regularization $\mathrm{Glimm}(A)$ of $\mathrm{Prim}(A)$ there exists $\alpha > 0$ such that $K\subset…

We answer a question of Takesaki by showing that the following can be derived from the thesis of N-T Shen: If A and B are sigma-unital hereditary C*-subalgebras of C such that ||p - q|| < 1, where p and q are the corresponding open…

A Hilbert $C^*$-quad module of finite type has a multi structure of Hilbert $C^*$-bimodules with two finite bases. We will construct a $C^*$-algebra from a Hilbert $C^*$-quad module of finite type and prove its universality subject to…

Let $M_{*}({\bf C})$ denote the C$^{*}$-algebra defined as the direct sum of all matrix algebras $\{M_{n}({\bf C}):n\geq 1\}$. It is known that $M_{*}({\bf C})$ has a non-cocommutative comultiplication $\Delta_{\varphi}$. We show that the…

On a separable C*-algebra A every (completely) bounded map, which preserves closed two sided ideals, can be approximated uniformly by elementary operators if and only if A is a finite direct sum of C*-algebras of continuous sections…

A study of Hilbert $C^*$-bimodules over commutative $C^*$-algebras is carried out and used to establish a sufficient condition for two quantum Heisenberg manifolds to be isomorphic.

We study the structure of certain classes of homologically trivial locally C*-algebras. These include algebras with projective irreducible Hermitian A-modules, biprojective algebras, and superbiprojective algebras. We prove that, if A is a…

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…

Given a correspondence X over a C*-algebra A, we construct a C*-algebra and a Hilbert C*-bimodule over it whose crossed product is isomorphic to the augmented Cuntz-Pimsner C*-algebra of X. This construction enables us to establish a…

Let A be a C*-algebra. It is shown that A is an AW*-algebra if, and only if, each maximal abelian self--adjoint subalgebra of A is monotone complete. An analogous result is proved for Rickart C*-algebras; a C*-algebra is a Rickart…

Several examples of (separable) C*-algebras with the property that their second (iterated) local multiplier algebra is strictly larger than the first have been found by various groups of authors over the past few years, thus answering a…

Main result: If a C*-algebra is simple, $\sigma$-unital, has finitely many extremal traces, and has strict comparison of positive elements by traces, then its multiplier also has strict comparison of positive elements by traces. The same…

It is shown that every linear surjective isometry between two right, full, Hilbert C*-modules is a sum of two maps : a (bi-) module map (which is completely isometric and preserves the inner product) and a map that reverses the (bi-) module…

We regard a right Hilbert C*-module X over a C*-algebra A endowed with an isometric *-homomorphism \phi: A\to L_A(X) as an object X_A of the C*-category of right Hilbert A-modules. Following a construction by the first author and Roberts,…

In this paper we present new structural information about the multiplier algebra Mult (A) of a sigma-unital purely infinite simple C*-algebra A, by characterizing the positive elements a in Mult(A) that are strict sums of projections…

We revisit the characterisation of modules over non-unital $C^*$-algebras analogous to modules of sections of vector bundles. A fullness condition on the associated multiplier module characterises a class of modules which closely mirror the…

We study uniform perturbations of intermediate C*-subalgebras of inclusions of simple C*-algebras. If a unital simple C*-algebra has a simple C*-subalgebra of finite index, then sufficiently close simple intermediate C*-subalgebras are…