Module Biflatness of the second dual of Banach algebras

2015/06/09 by Abasalt Bodaghi, Bodaghi, Abasalt, Ali Jabbari +1
Mathematics · #FOS: Mathematics #Functional Analysis (math.FA) #math.FA

paper · pdf · doi:10.48550/arxiv.1506.03035

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

arxiv created 2015/06/09 · arxiv updated 2015/06/10

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^** (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^** are module biflat, but which are not themselves module biflat.

Citations

• Module Biprojective and Module Biflat Banach Algebras

Related

• Module Biprojective and Module Biflat Banach Algebras
• Amenability for dual Banach algebras
• Arens regularity of module actions and weak amenability of Banach algebras
• Factorization property and Arens regularity
• Biflat-like Banach algebras