Module Biflatness of the second dual of Banach algebras

Abstract

Let $\mathcal{A}$ be a Banach algebra. Using the concept of module biflatness, we show that the module amenability of the second dual ${\mathcal{A}}^{\ast \ast }$ (with the first Arens product) necessitates the module amenability of $\mathcal{A}$. We give some examples of Banach algebras $\mathcal{A}$ such that ${\mathcal{A}}^{\ast \ast }$ are module biflat, but which are not themselves module biflat.

arXiv commentAccepted:Mathematical Reports. arXiv admin note: text overlap with arXiv:0912.4005

References in corpus (2)

• Module Biprojective and Module Biflat Banach Algebras
• Arens Regularity and Module Arens Regularity of Module Actions