Ideal Connes-Amenability of Lau Product of Banach Algebras

Abstract

Let A and B be Banach algebras and θ be a non-zero character on B. In the current paper, we study the ideal Connes-amenability of the algebra A ×θ B so-called the θ-Lau product algebra. We also prove that if A ×θ B is ideally Connes-amenable, then both A and B are ideally Connes-amenable. As a result, we show that l1(S) ×θ l1(S) is ideally Connes-amenable, where S is a Rees matrix semigroup.