Pseudo-amenability and pseudo-contractibility for certain products of Banach algebras

Abstract

Let A and B be two Banach algebras and let θ be a nonzero character on B. In this paper, we deal with the θ-Lau product A × θ B that was first introduced by A. T. Lau for certain Banach algebras known as Lau algebras and recently by M. S. Monfared for all Banach algebras; we study pseudo-amenability, pseudo-contractibility and character pseudo-amenability of A × θ B and their relations with A and B.

Characterization of homological properties of θ-Lau product of Banach algebras

“…Recently, Ghaderi et al in [8] studied pseudo-contractibility of θ-Lau product of Banach algebras. First, we give a simpler proof of [8,…”

“…In Section 4, we characterize pseudo-contractibility of θ-Lau product of Banach algebras. In [8], the authors addressed an open question whether or not A × θ B is pseudo-contractible if A is contractible and B is pseudo-contractible. Here, we give an affirmative answer to this question.…”

Johnson Pseudo-Contractibility and Pseudo-Amenability of θ-Lau Product

“…In the Section 3 we focus on pseudo-amenability of A × θ B. Pseudo-amenability of A × θ B was studied by E. Ghaderi et al [10]. They showed that pseudo-amenability of A × θ B implies pseudo-amenability of B, and implies pseudo-amenability of A whenever A has a bounded approximate identity.…”

Johnson pseudo-contractibility and pseudo-amenability of $ θ$-Lau product of Banach algebras

“…was studied by E. Ghaderi et al in [10]. They prove that pseudo-amenability of A × θ B implies pseudo-amenability of B, and implies pseudo-amenability of A whenever A has a bounded approximate 2010 Mathematics Subject Classification.…”