Arens regularity and amenability of lau product of banach algebras defined by a banach algebra morphism

摘要

Given a morphism T from a Banach algebra B to a commutative Banach algebra A, a multiplication is defined on the Cartesian product space A×B perturbing the coordinatewise product resulting in a new Banach algebra × _TB. The Arens regularity as well as amenability (together with its various avatars) of A× TB are shown to be stable with respect to T.