Strong pseudo-Connes amenability of dual Banach algebras

2018/07/30 by S. F. Shariati, Shariati, S. F., A. Pourabbas +3
Mathematics · #Advanced Banach Space Theory #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Functional Analysis (math.FA)

paper · pdf · doi:10.48550/arxiv.1807.11556

openalex publication_date 2018/07/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we introduce the new notion of strong pseudo-Connes amenability for dual Banach algebras. We study the relation between this new notion to the various notions of Connes amenability. Also we show that for every non-empty set I, M_I(ℂ) is strong pseudo-Connes amenable if and only if I is finite. We provide some examples of certain dual Banach algebras and we study its strong pseudo-Connes amenability. In the last section, we investigate the property ultra central approximate identity for a Banach algebra A and its second dual A^**. Also we show that for a left cancellative regular semigroup S, ℓ¹(S)^** has an ultra central approximat identity if and only if S is a group. Finally we study this property for φ-Lau product Banach algebras and the module extension Banach algebras.

Related

• Johnson pseudo-Connes amenability of dual Banach algebras
• Weakly Connes amenable dual Banach algebras
• Amenability for dual Banach algebras
• Approximate Connes-amenability of dual Banach algebras
• Pointwise amenability for dual Banach algebras