Weak amenability and 2-weak amenability of Beurling algebras

Details Weak amenability and 2-weak amenability of Beurling algebras Weak amenability and 2-weak amenability of Beurling algebras

2007-05-31

arxiv.org/abs/0706.0038v2

Mathematics

Functional Analysis

25 pages

Scientific paper

Let $L^1_\om(G)$ be a Beurling algebra on a locally compact abelian group $G$. We look for general conditions on the weight which allows the vanishing of continuous derivations of $L^1_\om(G)$. This leads us to introducing vector-valued Beurling algebras and considering the translation of operators on them. This is then used to connect the augmentation ideal to the behavior of derivation space. We apply these results to give examples of various classes of Beurling algebras which are weakly amenable, 2-weakly amenable or fail to be even 2-weakly amenable.

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