Essential Amenability of Dual Banach Algebras

Abstract

We show that an essentially amenable Banach algebra need not have an approximate identity. This answers a question posed by Ghahramani and Loy [‘Generalized notions of amenability’, J. Funct. Anal. 208 (2004), 229–260]. Essentially Connes-amenable dual Banach algebras are introduced and studied.

Weakly Connes amenable dual Banach algebras

“…Then V equipped with the product defined by ab := f (a)b for a, b ∈ V, is a noncommutative Banach algebra denoted by V f . Moreover, if V is a dual Banach space and if f is w * -continuous, then V f is a dual Banach algebra, see for instance [18]. Proposition 4.8.…”