More on cyclic amenability of the Lau product of Banach algebras defined by a Banach algebra morphism

Abstract

Abstract For two Banach algebras A and B, the T-Lau product A× T B, was recently introduced and studied for some bounded homomorphism T : B → A with ∥T∥ ≤ 1. Here, we give general nessesary and sufficent conditions for A× T B to be (approximately) cyclic amenable. In particular, we extend some recent results on (approximate) cyclic amenability of direct product A ⊕ B and T-Lau product A× T B and answer a question on cyclic amenability of A× T B.