Module amenability of Banach algebras

In this monograph, some new notions of module amenability such as module contractibility, module character amenability and n-weak module amenability for Banach algebras are introduced and some hereditary properties are given. For an inverse semigroup S with subsemigroup E of idempotents, module character amenability of the semigroup algebra l^1(S) is shown to be equivalent to S being amenable. Also, it is proved that l^1(S) is permanently weakly module amenable. The concept of module Arens regularity for Banach algebras and bilinear maps are introduced and they are characterized. The module topological centers of second dual of a Banach algebra are defined and they are found for l^1(S) . It is proved that l^1 (S) is module amenable (as an l^1(E)-module) if and only if a maximal group homomorphic image of S is finite. Finally, it is shown under what conditions l^1(S) is module biflat and module biprojective.

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Abasalt Bodaghi is Assistant Professor of Mathematics at Islamic Azad University. He received his PhD from Science and Research Branch(IAU) in 2009. His publications include several papers in international journals. In 2011, he was also awarded Excellent Performance Award from INSPEM in UPM. His area of interest are Harmonic Analysis and Stability.