arXiv subjects
Publications and source records attributed to Fereidoun Ghahramani.
We prove that pseudo-amenability implies approximate amenability for Banach algebras with a bounded approximate identity. Consequently, these two notions of generalized amenability are equivalent for such Banach algebras. Our proof closes a gap in the paper by F. Ghahramani and Y. Zhang, Pseudo-amenable and pseudo-contractible Banach algebras.
Amenability of any of the algebras described in the title is known to force them to be finite-dimensional. The analogous problems for \emph{approximate} amenability have been open for some years now. In this article we give a complete solution for the first two classes, using a new criterion for showing that certain Banach algebras without bounded approximate identities cannot be approximately amenable. The method also provides a unified approach to existing non-approximate amenability results, and is applied to the study of certain commutative Segal algebras. Using different techniques, we prove that \emph{bounded} approximate amenability of the second dual of a Fourier algebra implies that it is finite-dimensional. Some other results for related algebras are obtained.