Weak amenability for the second dual of Banach modules

Abstract

Let A be a Banach algebra, E be a Banach A-bimodule and W E ! A be a bounded Banach A-bimodule homomorphism. It is shown that under some mild conditions, the weak 00 -amenability of E 00 (as an A 00 -bimodule) necessitates weak -amenability of E (as an A-bimodule). Some examples of weak -amenable Banach modules are provided as well.