Related papers: Factorization property and Arens regularity

Let $\omega $ be a weight function on a locally compact group G mand let $ M_* (G, \omega ) $ be the subspace of $ M(G , \omega )^* $ consisting of all functionals that vanish at infinity. In this paper, we first investigate the Arens…

In this paper we define module biprojctivity and module biflatness for a Banach algebra which is a Banach module over another Banach algebra with compatible actions, and find their relation to classical biprojectivity and biflatness. As a…

Let $\mathcal{A}$ be a $C^*$-algebra, and consider the Banach algebra $\mathcal{A} \otimes_\gamma \mathcal{A}$, where $\otimes_\gamma$ denotes the projective Banach space tensor product; if $\mathcal{A}$ is commutative, this is the…

For a Banach algebra $A$ with a bounded approximate identity, we investigate the $A$-module homomorphisms of certain introverted subspaces of $A^*$, and show that all $A$-module homomorphisms of $A^*$ are normal if and only if $A$ is an…

Garth Dales asked whether a Banach algebra $\mathcal{A}$ having an Arens regular closed ideal $\mathcal{J}$ with Arens regular quotient $\mathcal{A}/\mathcal{J}$ is necessarily Arens regular. We prove in this note that, for a class of…

Associated with a locally compact group $\cal G$ and a $\cal G$-space $\cal X$ there is a Banach subspace $LUC({\cal X},{\cal G})$ of $C_b({\cal X})$, which has been introduced and studied by Lau and Chu in \cite{chulau}. In this paper, we…

This article is intended towards the study of the bidual of generalized group algebra $L^1(G,\mA)$ equipped with two Arens product, where $G$ is any locally compact group and $\mA$ is a Banach algebra. We show that the left topological…

We define a Banach algebra A to be dual if $A = (A_\ast)^\ast$ for a closed submodule $A_\ast$ of $A^\ast$. The class of dual Banach algebras includes all $W^\ast$-algebras, but also all algebras M(G) for locally compact groups G, all…

In this article, we will give a characterization of Banach bimodules over $C^*$-algebras of compact operators that arises from operator spaces as well as a characterization of (F)-Banach bundles amongst all (H)-Banach bundles over a…

Let G be a locally compact group. Consider the Banach algebra L_1(G)^**, equipped with the first Arens multiplication, as well as the algebra LUC(G)^*, the dual of the space of bounded left uniformly continuous functions on G, whose product…

Let WAP(A) be the space of all weakly almost periodic functionals on a Banach algebra A. The Banach algebra A for which the natural embedding of A into WAP(A)* is bounded below is called a WAP-algebra. We show that the second dual of a…

The theory of M-ideals and multiplier mappings of Banach spaces naturally generalizes to left (or right) M-ideals and multiplier mappings of operator spaces. These subspaces and mappings are intrinsically characterized in terms of the…

We investigate the interaction between Arens products on the bidual of a Banach algebra and structural regularity properties of functionals on the algebra. Building on the classical characterization of weakly almost periodic functionals via…

We investigate the automatic regularity of bounded derivations from a Banach lattice algebra of regular operators A into a Banach A-module with a Banach lattice structure compatible with the module operations.

The theory of multiplier modules of Hilbert C*-modules is reconsidered to obtain more properties of these special Hilbert C*-modules. The property of a Hilbert C*-module to be a multiplier C*-module is shown to be an invariant with respect…

The notions of module pseudo-amenable and module pseudo-contractible Banach algebras are introduced. For a Banach algebra with bounded approximate identity, module pseudo-amenability and module approximate amenability are the same…

Motivated by the study of von Neumann regular skew groups as carried out by Alfaro, Ara and del Rio in 1995 we investigate regular and biregular Hopf module algebras. If $A$ is an algebra with an action by an affine Hopf algebra $H$, then…

We show that the amenability of a locally compact group $G$ is equivalent to a factorization property of $VN(G)$ which is given by $ VN(G) = <VN(G)^*VN(G)>$. This answer partially two problems proposed by Z. Hu and M. Neufang in their…

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…

In this paper, we study the hereditary properties of module $(\phi,\varphi)$-amenability on Banach algebras. We also define the concept of module character contractibility for Banach algebras and obtain characterizations of module character…