Related papers: Weak Centrality for Certain Tensor Products of $C^…

We analyze certain algebraic structures of the Banach space projective tensor product of $C^*$-algebras which are comparable with their known counterparts or the Haagerup tensor product and the operator space projective tensor product of…

For $C^{*}$-algebras $A$ and $B$, the operator space projective tensor product $A\hat{\otimes}B$ and the Banach space projective tensor product $A\otimes_{\gamma}B$ are shown to be symmetric. We also show that $A\hat{\otimes}B$ is weakly…

In this paper we introduce the notion of $\Delta$-weak character amenable Banach algebras and investigate $\Delta$-weak character amenability of certain Banach algebras such as projective tensor product $A\widehat{\otimes}B$, Lau product…

The category of $C^*$-algebras is blessed with many different tensor products. In contrast, virtually the only tensor product ever used in the category of von Neumann algebras is the normal spatial tensor product. We propose a definition of…

In this note, we study the Arens regularity of projective tensor product $A\hat{\otimes}B$ whenever $A$ and $B$ are Arens regular. We establish some new conditions for showing that the Banach algebras $A$ and $B$ are Arens regular if and…

We give a number of equivalent conditions (including weak centrality) for a general $C^*$-algebra to have the centre-quotient property. We show that every $C^*$-algebra $A$ has a largest weakly central ideal $J_{wc}(A)$. For an ideal $I$ of…

We first prove that every AF-algebra is weakly central, thereby resolving a question left open by Archbold--Gogi\'c. We then establish a new characterization of weak centrality for unital $C^*$-algebras in terms of $C(X)$-algebras. The…

We study tensor products of a $C_0 (X)$-algebra $A$ and a $C_0 (Y)$-algebra $B$, and analyse the structure of their minimal tensor product $A \otimes B$ as a $C_0 (X \times Y)$-algebra. We show that when $A$ and $B$ define continuous…

For a simple $C^*$-algebra $A$ and any other $C^*$-algebra $B$, it is proved that every closed ideal of $A \otimes^{\min} B$ is a product ideal if either $A$ is exact or $B$ is nuclear. Closed commutator of a closed ideal in a Banach…

The Banach $^{*}$-algebra $A\hat{\otimes}B$, the operator space projective tensor product of $C^{*}$-algebras $A$ and $B$, is shown to be $^{*}$-regular if Tomiyama's property ($F$) holds for $A\otimes_{\min}B$ and $A \otimes_{\min}B=A…

Given a Hausdorff compact space X, we study the C^*-(semi)-norms on the algebraic tensor product $A\otimes_{alg,C(X)} B$ of two C(X)-algebras A and B over C(X). In particular, if one of the two C(X)-algebras defines a continuous field of…

We study the property of being strongly weakly compactly generated (and some relatives) in projective tensor products of Banach spaces. Our main result is as follows. Let $1<p,q<\infty$ be such that $1/p+1/q\geq 1$. Let $X$ (resp., $Y$) be…

We identify all closed Lie ideals of $A \otimes^{\alpha} B$ and $B(H) \otimes^{\alpha} B(H)$, where $\otimes^{\alpha}$ is either the Haagerup tensor product, the Banach space projective tensor product or the operator space projective tensor…

We construct several new classes of bifunctors $(A,B)\mapsto A\otimes_{\alpha} B$, where $A\otimes_\alpha B$ is a cross norm completion of $A\odot B$ for each pair of C*-algebras $A$ and $B$. For the first class of bifunctors considered…

We prove that, under certain conditions, uniform weak mixing (to zero) of the bounded sequences in Banach space implies uniform weak mixing of its tensor product. Moreover, we prove that ergodicity of tensor product of the sequences in…

Let $X$ be a left introverted subspace of dual of a Banach algebra. We study $Z_t(X^*),$ the topological center of Banach algebra $X^*$. We fined the topological center of $(X\cA)^*$, when $\cA$ has a bounded right approximate identity and…

We study weak amenability of central Beurling algebras $ZL^1(G,\omega)$. The investigation is a natural extension of the known work on the commutative Beurling algebra $L^1(G,\omega)$. For [FC]$^-$ groups we establish a necessary condition…

In this short note, we prove that the set of elementary tensors is weakly closed in the projective tensor product of two Banach spaces. As a result, we are able to answer a question from the literature proving that if $(x_n) \subset X$ and…

Following up on previous work, we prove a number of results for C*-algebras with the weak ideal property or topological dimension zero, and some results for C*-algebras with related properties. Some of the more important results include:…

For $C^*$-algebras $A$ and $B$, we prove the slice map conjecture for ideals in the operator space projective tensor product $A \hat\otimes B$. As an application, a characterization of prime ideals in the Banach $\ast$-algebra $A\hat\otimes…