Related papers: A note on approximately biflat banach algebras

In this paper, we investigate homological properties of Banach algebras. We show that retractions Banach algebras preserve biprojectivity, contractibility and biflatness. We also prove that contractibility of second dual of a Banach algebra…

Let $G$ be an amenable group. We define and study an algebra $\mathcal{A}_{sn}(G)$, which is related to invariant means on the subnormal subgroups of $G$. For a just infinite amenable group $G$, we show that $\mathcal{A}_{sn}(G)$ is…

Banach algebra A for which the natural embedding x into x^ of A into WAP(A)* is bounded below; that is, for some m in R with m > 0 we have ||x^|| > m ||x||, is called a WAP-algebra. Through we mainly concern with weighted measure algebra…

We study various operator homological properties of the Fourier algebra $A(G)$ of a locally compact group $G$. Establishing the converse of two results of Ruan and Xu, we show that $A(G)$ is relatively operator 1-projective if and only if…

New notion of weak amenability, $(\varphi,\psi)$-weak amenability recently introduced. In this paper we consider this new notion and study $(\varphi,\psi)$-weak amenability of group algebras $M(G)$, $L^1(G)$ and $S^1(G)$.

We study when certain properties of Banach algebras are stable under ultrapower constructions. In particular, we consider when every ultrapower of $\mc A$ is Arens regular, and give some evidence that this is if and only if $\mc A$ is…

We show that if $T$ is an isometry (as metric spaces) from an open subgroup of the group of the invertible elements in a unital semisimple commutative Banach algebra onto an open subgroup of the group of the invertible elements in a unital…

A dual Banach algebra is a Banach algebra which is a dual space, with the multiplication being separately weak$^*$-continuous. We show that given a unital dual Banach algebra $\mc A$, we can find a reflexive Banach space $E$, and an…

Given a Banach space $A$ and fix a non-zero $\varphi\in A^*$ with $\|\varphi\|\leq 1$. Then the product $a\cdot b=\langle\varphi, a\rangle\ b$ turning $A$ into a Banach algebra which will be denoted by $_\varphi A.$ Some of the main…

We prove that the crossed product Banach algebra $\ell^1(A,G,\alpha)$ that is associated with a $\mathrm{C}^\ast$-dynamical system $(A,G,\alpha)$ is amenable if $G$ is a discrete amenable group and $A$ is a commutative or finite dimensional…

In this paper we prove that if (A,\pi) is an amenable Banach algebra and if \rho is another Banach algebra multiplication on A such that the difference between \rho and and \pi is less than 1/11, then (A, \rho) is also amenable.

We show that if $T$ is an isometry (as metric spaces) from an open subgroup of the invertible group $A^{-1}$ of a unital Banach algebra $A$ onto an open subgroup of the invertible group $B^{-1}$ of a unital Banach algebra $B$, then $T$ is…

Let ${\mathcal A}$ and ${\frak A}$ be Banach algebras such that ${\mathcal A}$ is a Banach ${\frak A}$-bimodule with compatible actions. We define the product ${\cal A}\rtimes{\frak A}$, which is a strongly splitting Banach algebra…

We investigate when discrete, amenable groups have $C^*$-algebras of real rank zero. While it is known that this happens when the group is locally finite, the converse in an open problem. We show that if $C^*(G)$ has real rank zero, then…

We shall develop a notion of amenability for dual Banach algebras, namely weak Connes amenability, which will play the role that weak amenability does for usual Banach algebras

Assume that $A$, $B$ are Banach algebras and $m:A\times B\to B$, $m^\prime:A\times A\to B$ are bounded bilinear mappings. We will study the relation between Arens regularities of $m$, $m^\prime$ and the Banach algebras $A$, $B$. For Banach…

It is known that locally compact groups approximable by finite ones are unimodular, but this condition is not sufficient, for example, the simple Lie groups are not approximable by finite ones as topological groups. In this paper the…

The paper deals with continuous homomorphisms $S \ni s \mapsto T_s \in L(E)$ of amenable semigroups $S$ into the algebra $L(E)$ of all bounded linear operators on a Banach space $E$. For a closed linear subspace $F$ of $E$, sufficient…

We answer, by counterexample, several open questions concerning algebras of operators on a Hilbert space. The answers add further weight to the thesis that, for many purposes, such algebras ought to be studied in the framework of operator…

In this paper, we study the weak amenability of weighted measure algebras and prove that $M(G, \omega)$ is weakly amenable if and only if $G$ is discrete and every bounded quasi-additive function is inner. We also study the weak amenability…