A Generalization of the Weak Amenability of some Banach Algebra

2010/11/03 by Kazem Haghnejad, Haghnejad, Kazem
Mathematics · #Advanced Banach Space Theory #Advanced Operator Algebra Research #Advanced Topics in Algebra #math.GR

paper · pdf · doi:10.48550/arxiv.1011.0802

arxiv created 2010/11/03 · arxiv updated 2010/11/04

Abstract

Let A be a Banach algebra and A^** be the second dual of it. We show that by some new conditions, A is weakly amenable whenever A^** is weakly amenable. We will study this problem under generalization, that is, if (n+2)-th dual of A, A⁽ⁿ⁺²⁾, is T-S-weakly amenable, then A⁽ⁿ⁾ is T-S-weakly amenable where T and S are continuous linear mappings from A⁽ⁿ⁾ into A⁽ⁿ⁾.

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