JOHNSON PSEUDO-CONNES AMENABILITY OF DUAL BANACH ALGEBRAS

Abstract

We introduce the notion of Johnson pseudo-Connes amenability for dual Banach
algebras. We study the relation between this new notion with the various notions of Connes
amenability like Connes amenability, approximate Connes amenability and pseudo Connes
amenability. We also investigate some hereditary properties of this new notion. We prove
that for a locally compact group G, M(G) is Johnson pseudo-Connes amenable if and only if
G is amenable. Also we show that for every non-empty set I, MI(C) under this new notion is
forced to have a finite index. Finally, we provide some examples of certain dual Banach algebras
and we study their Johnson pseudo-Connes amenability.