Displaying similar documents to “A generalization of the n -weak amenability of Banach 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 } .

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.

Derivations into iterated duals of Banach algebras

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

Studia Mathematica

Similarity:

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

Similarity:

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 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.