Diagonals of Lau product Banach algebras

Abstract

In this paper, we study and compare the types of diagonals for Lau product Banach algebras [Formula: see text] and diagonals of two Banach algebras [Formula: see text] and [Formula: see text], where [Formula: see text] is a homomorphism from [Formula: see text] to [Formula: see text]. As a consequence, we obtain the (approximate) amenability and contractibility [Formula: see text] in terms of (approximate) amenability and contractibility of [Formula: see text] and [Formula: see text]. Moreover, we introduce the notion of pseudo-virtual diagonal for a Banach algebra and present some characterization results for Lau product Banach algebras.