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Displaying similar documents to “Module structures on iterated duals of Banach algebras.”

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.

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., 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;...

Problems concerning n -weak amenability of a Banach algebra

Alireza Medghalchi, Taher Yazdanpanah (2005)

Czechoslovak Mathematical Journal

Similarity:

In this paper we extend the notion of n -weak amenability of a Banach algebra 𝒜 when 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 .

Module Connes amenability of hypergroup measure algebras

Massoud Amini (2015)

Open Mathematics

Similarity:

We define the concept of module Connes amenability for dual Banach algebras which are also Banach modules with a compatible action. We distinguish a closed subhypergroup K0 of a locally compact measured hypergroup K, and show that, under different actions, amenability of K, M.K0/-module Connes amenability of M.K/, and existence of a normal M.K0/-module virtual diagonal are related.