Connes amenability of the second dual of Arens regular Banach algebras

Abstract

In this paper we study the Connes amenability of the second dual of Arens regular Banach algebras. Of course we provide a partial answer to the question posed by Volker Runde. Also we fined the necessary and sufficient conditions for the second dual of an Arens regular module extension Banach algebra to be Connes amenable when the module is reflexive.

arXiv comment5 pages. To appear in Italian J. of Pure and Appl. Math