Displaying similar documents to “A characterization of weakly amenable Banach algebras”

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.

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;...

Amenability and the second dual of a Banach algebra

Frédéric Gourdeau (1997)

Studia Mathematica

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Amenability and the Arens product are studied. Using the Arens product, derivations from A are extended to derivations from A**. This is used to show directly that A** amenable implies A amenable.

On φ-inner amenable Banach algebras

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

Colloquium Mathematicae

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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.

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...