Related papers: Module super-amenability for semigroup algebras

We introduce two notions of amenability for a Banach algebra $\cal A$. Let $I$ be a closed two-sided ideal in $\cal A$, we say $\cal A$ is $I$-weakly amenable if the first cohomology group of $\cal A$ with coefficients in the dual space…

We present new additive results for the pseudo core inverse in a Banach algebra with involution. The necessary and sufficient conditions under which the sum of two pseudo core invertible elements in Banach *-algebra is pseudo core…

We consider modules E over a C*-algebra A which are equipped with a map into A_+ that has the formal properties of a norm. We completely determine the structure of these modules. In particular, we show that if A has no nonzero commutative…

Let $\A$ be a semisimple unital commutative Banach algebra. We say that a Banach $\A$-module $M$ is nice if every proper closed submodule of $M$ is contained in a closed submodule of $M$ of codimension 1. We provide examples of nice and…

We study Johnson amenability for unconditional direct sums of Banach algebras. Given a family $(A_i)_{i\in I}$ of Banach algebras and a Banach sequence lattice $E$ on~$I$, the $E$-sum $\bigl(\bigoplus_{i\in I} A_i\bigr)_{\!E}$ carries a…

Let $K$ denote a locally compact commutative hypergroup, $L^1(K)$ the hypergroup algebra, and $\alpha$ a real-valued hermitian character of $K$. We show that $K$ is $\alpha$-amenable if and only if $L^1(K)$ is $\alpha$-left amenable. We…

For a commutative semi-simple Banach algebra ${A}$ which is an ideal in its second dual we give a necessary and sufficient condition for an essential abstract Segal algebra in ${A}$ to be a BSE-algebra. We show that a large class of…

We give a criterion ensuring that the elementary class of a modular Banach space E (that is, the class of Banach spaces, some ultrapower of which is linearly isometric to an ultrapower of E) consists of all direct sums E\oplus_m H, where H…

In this paper we prove a general convergence theorem for almost-additive set functions on unimodular, amenable groups. These mappings take their values in some Banach space. By extending the theory of epsilon-quasi tiling techniques, we set…

It is proved that in a commutative unital Banach algebra, every non-maximal closed prime ideal is accessible. Specifically, it can be represented as the intersection of all closed ideals of the algebra that properly contain it.…

It was noticed recently that, given a metric space $(X,d_X)$, the equivalence classes of metrics on the disjoint union of the two copies of $X$ coinciding with $d_X$ on each copy form an inverse semigroup $M(X)$ with respect to…

We review and analyse techniques from the literature for extending a normed algebra, A to a normed algebra, B, so that B has interesting or desirable properties which A may lack. For example, B might include roots of monic polynomials over…

We prove that for every group $G$ and any two sets $I,J$, the Brandt semigroup algebras $\ell(B(I,G))$ and $\ell(B(J,G))$ are Morita equivalent with respect to the Morita theory of self-induced Banach algebras introduced by Gronbaek. As…

Let $A$ and $B$ be Banach algebras and let $B$ be an algebraic Banach $A-$bimodule. Then the $\ell^1-$direct sum $A\times B$ equipped with the multiplication $$(a_1,b_1)(a_2,b_2)=(a_1a_2,a_1\cdot b_2+b_1\cdot a_2+b_1b_2),~~ (a_1, a_2\in A,…

Associated to a nonzero homomorphism $\varphi$ of a Banach algebra $A$, we regard special functionals, say $m_\varphi$, on certain subspaces of $A^\ast$ which provide equivalent statements to the existence of a bounded right approximate…

We examine the condition that a complex Banach algebra $A$ have dense invertible group. We show that, for commutative algebras, this property is preserved by integral extensions. We also investigate the connections with an old problem in…

If $D:A \to X$ is a derivation from a Banach algebra to a contractive, Banach $A$-bimodule, then one can equip $X^{**}$ with an $A^{**}$-bimodule structure, such that the second transpose $D^{**}: A^{**} \to X^{**}$ is again a derivation.…

We introduce the notions of approximate Connes-amenability and approximate strong Connes-amenability for dual Banach algebras. Then we characterize these two types of algebras in terms of approximate normal virtual diagonals and approximate…

Let $\Lambda\subset[0,\infty)$ be an additive semigroup with $0\in\Lambda$, $\omega$ be an admissible weight on $\Lambda$, $\mathcal A$ be a unital Banach algebra, and let $f(s)=\sum_{\lambda\in\Lambda} f_\lambda e^{-\lambda s}$ for…

This paper is a continuation of our study of compact, power compact, Riesz, and quasicompact endomorphisms of commutative Banach algebras. Previously it has been shown that if $B$ is a unital commutative semisimple Banach algebra with…