Weak amenability of the second dual of a Banach algebra

M. Eshaghi Gordji; M. Filali

The search session has expired. Please query the service again.

Displaying similar documents to “Weak amenability of the second dual of a Banach algebra”

Amenability for dual Banach algebras

V. Runde (2001)

Studia Mathematica

Similarity:

We define a Banach algebra 𝔄 to be dual if 𝔄 = (𝔄⁎)* for a closed submodule 𝔄⁎ of 𝔄*. The class of dual Banach algebras includes all W*-algebras, but also all algebras M(G) for locally compact groups G, all algebras ℒ(E) for reflexive Banach spaces E, as well as all biduals of Arens regular Banach algebras. The general impression is that amenable, dual Banach algebras are rather the exception than the rule. We confirm this impression. We first show that under certain conditions...

Constructions preserving $n$ -weak amenability of Banach algebras

A. Jabbari, Mohammad Sal Moslehian, H. R. E. Vishki (2009)

Mathematica Bohemica

Similarity:

A surjective bounded homomorphism fails to preserve $n$ -weak amenability, in general. We however show that it preserves the property if the involved homomorphism enjoys a right inverse. We examine this fact for certain homomorphisms on several Banach algebras.

Ideal amenability of module extensions of Banach algebras

Eshaghi M. Gordji, F. Habibian, B. Hayati (2007)

Archivum Mathematicum

Similarity:

Let $𝒜$ be a Banach algebra. $𝒜$ is called ideally amenable if for every closed ideal $I$ of $𝒜$ , the first cohomology group of $𝒜$ with coefficients in $I^{*}$ is zero, i.e. $H^{1} (𝒜, I^{*}) = {0}$ . Some examples show that ideal amenability is different from weak amenability and amenability. Also for $n \in N$ , $𝒜$ is called $n$ -ideally amenable if for every closed ideal $I$ of $𝒜$ , $H^{1} (𝒜, I^{(n)}) = {0}$ . In this paper we find the necessary and sufficient conditions for a module extension Banach algebra to be 2-ideally amenable.

On φ-inner amenable Banach algebras

A. Jabbari, T. Mehdi Abad, M. Zaman Abadi (2011)

Colloquium Mathematicae

Similarity:

Generalizing the concept of inner amenability for Lau algebras, we define and study the notion of φ-inner amenability of any Banach algebra A, where φ is a homomorphism from A onto ℂ. Several characterizations of φ-inner amenable Banach algebras are given.

On the weak amenability of ℬ(X)

A. Blanco (2010)

Studia Mathematica

Similarity:

We investigate the weak amenability of the Banach algebra ℬ(X) of all bounded linear operators on a Banach space X. Sufficient conditions are given for weak amenability of this and other Banach operator algebras with bounded one-sided approximate identities.

Some notions of amenability for certain products of Banach algebras

Eghbal Ghaderi, Rasoul Nasr-Isfahani, Mehdi Nemati (2013)

Colloquium Mathematicae

Similarity:

For two Banach algebras and ℬ, an interesting product $\times_{θ} ℬ$ , called the θ-Lau product, was recently introduced and studied for some nonzero characters θ on ℬ. Here, we characterize some notions of amenability as approximate amenability, essential amenability, n-weak amenability and cyclic amenability between and ℬ and their θ-Lau product.

Solved and unsolved problems in generalized notions of amenability for Banach algebras

Yong Zhang (2010)

Banach Center Publications

Similarity:

We survey the recent investigations on approximate amenability/contractibility and pseudo-amenability/contractibility for Banach algebras. We will discuss the core problems concerning these notions and address the significance of any solutions to them to the development of the field. A few new results are also included.

A commutativity theorem for Banach algebras

Donald Z. Spicer (1973)

Colloquium Mathematicae

Similarity:

Dual Banach algebras: representations and injectivity

Matthew Daws (2007)

Studia Mathematica

Similarity:

We study representations of Banach algebras on reflexive Banach spaces. Algebras which admit such representations which are bounded below seem to be a good generalisation of Arens regular Banach algebras; this class includes dual Banach algebras as defined by Runde, but also all group algebras, and all discrete (weakly cancellative) semigroup algebras. Such algebras also behave in a similar way to C*- and W*-algebras; we show that interpolation space techniques can be used in place of...

A generalized notion of $n$ -weak amenability

Abasalt Bodaghi, Behrouz Shojaee (2014)

Mathematica Bohemica

Similarity:

In the current work, a new notion of $n$ -weak amenability of Banach algebras using homomorphisms, namely $(ϕ, ψ)$ - $n$ -weak amenability is introduced. Among many other things, some relations between $(ϕ, ψ)$ - $n$ -weak amenability of a Banach algebra $𝒜$ and $M_{m} (𝒜)$ , the Banach algebra of $m \times m$ matrices with entries from $𝒜$ , are studied. Also, the relation of this new concept of amenability of a Banach algebra and its unitization is investigated. As an example, it is shown that the group algebra $L^{1} (G)$ is ( $ϕ, ψ$ )- $n$ -weakly amenable...

Approximate amenability of semigroup algebras and Segal algebras

H. G. Dales, R. J. Loy

Similarity:

In recent years, there have been several studies of various ’approximate’ versions of the key notion of amenability, which is defined for all Banach algebras; these studies began with work of Ghahramani and Loy in 2004. The present memoir continues such work: we shall define various notions of approximate amenability, and we shall discuss and extend the known background, which considers the relationships between different versions of approximate amenability. There are a number of open...

Approximate and weak amenability of certain Banach algebras

P. Bharucha, R. J. Loy (2010)

Studia Mathematica

Similarity:

The notions of approximate amenability and weak amenability in Banach algebras are formally stronger than that of approximate weak amenability. We demonstrate an example confirming that approximate weak amenability is indeed actually weaker than either approximate or weak amenability themselves. As a consequence, we examine the (failure of) approximate amenability for $ℓ^{p}$ -sums of finite-dimensional normed algebras.

Weak $^{*}$ -continuous derivations in dual Banach algebras

M. Eshaghi-Gordji, A. Ebadian, F. Habibian, B. Hayati (2012)

Archivum Mathematicum

Similarity:

Let $𝒜$ be a dual Banach algebra. We investigate the first weak $^{*}$ -continuous cohomology group of $𝒜$ with coefficients in $𝒜$ . Hence, we obtain conditions on $𝒜$ for which $H_{w^{*}}^{1} (𝒜, 𝒜) = {0} .$