Amenability and the second dual of a Banach algebra

Frédéric Gourdeau

Displaying similar documents to “Amenability and the second dual of a Banach algebra”

Module structures on iterated duals of Banach algebras.

Bodaghi, A., Ettefagh, M., Eshaghi Gordji, M., Medghalchi, A.R. (2010)

Analele Ştiinţifice ale Universităţii “Ovidius" Constanţa. Seria: Matematică

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Constructions preserving $n$ -weak amenability of Banach algebras

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

Mathematica Bohemica

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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.

A characterization of weakly amenable Banach algebras

Niels Groenbaek (1989)

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Derivations into iterated duals of Banach algebras

H. Dales, F. Ghahramani, N. Grønbæek (1998)

Studia Mathematica

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We introduce two new notions of amenability for a Banach algebra A. The algebra A is n-weakly amenable (for n ∈ ℕ) if the first continuous cohomology group of A with coefficients in the n th dual space $A^{(n)}$ is zero; i.e., $ℋ^{1} (A, A^{(n)}) = 0$ . Further, A is permanently weakly amenable if A is n-weakly amenable for each n ∈ ℕ. We begin by examining the relations between m-weak amenability and n-weak amenability for distinct m,n ∈ ℕ. We then examine when Banach algebras in various classes are n-weakly amenable;...

3-Weak amenability of (2n)th duals of Banach algebras

Mina Ettefagh (2012)

Colloquium Mathematicae

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We show that under some conditions, 3-weak amenability of the (2n)th dual of a Banach algebra A for some n ≥ 1 implies 3-weak amenability of A.

A generalization of the $n$ -weak amenability of Banach algebras.

Mewomo, O.T., Akinbo, G. (2011)

Analele Ştiinţifice ale Universităţii “Ovidius" Constanţa. Seria: Matematică

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On the weak amenability of ℬ(X)

A. Blanco (2010)

Studia Mathematica

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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.

Fixed point characterization of left amenable Lau algebras.

Nasr-Isfahani, R. (2004)

International Journal of Mathematics and Mathematical Sciences

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Problems concerning $n$ -weak amenability of a Banach algebra

Alireza Medghalchi, Taher Yazdanpanah (2005)

Czechoslovak Mathematical Journal

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In this paper we extend the notion of $n$ -weak amenability of a Banach algebra $𝒜$ when $n \in ℕ$ . Technical calculations show that when $𝒜$ is Arens regular or an ideal in $𝒜^{* *}$ , then $𝒜^{*}$ is an $𝒜^{(2 n)}$ -module and this idea leads to a number of interesting results on Banach algebras. We then extend the concept of $n$ -weak amenability to $n \in ℤ$ .

Weak amenability of the second dual of a Banach algebra

M. Eshaghi Gordji, M. Filali (2007)

Studia Mathematica

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It is known that a Banach algebra inherits amenability from its second Banach dual **. No example is yet known whether this fails if one considers the weak amenability instead, but the property is known to hold for the group algebra L¹(G), the Fourier algebra A(G) when G is amenable, the Banach algebras which are left ideals in **, the dual Banach algebras, and the Banach algebras which are Arens regular and have every derivation from into * weakly compact. In this paper, we extend this...