Enveloping Dual Banach Algebras and Approximate Properties

Abstract

Suppose that A is a Banach algebra and FA is its enveloping dual Banach algebra, we show that FA is approximately contractible (approximately amenable) if A has the same property. Also, we study the relation between the pseudoamenability of FA and the pseudoamenability of the second dual A∗∗ and we also characterize approximate biflatness and approximate biprojectivity of FA associated with approximate biflatness and approximate biprojectivity of the second dual A∗∗.