Essential character cones amenability

Abstract

In the present paper we introduce and study the concept of essential -Connes-amenability of a dual Banach algebra , where  the set of all -continuous elements of . We show that under certain conditions, essential -Connes-amenability and -Connes amenability are equivalent. Moreover we prove some hereditary properties and investigate essential -Connes amenability for a certain class of Banach algebras.