On φ-Connes Module Amenability of Dual Banach Algebrasand φ-splitting

In this paper, we define φ-Connes module amenability of a dual Banachalgebra A, where φ is a ω∗-continuous bounded module homomorphism from A ontoitself. We obtain the relation between φ-Connes module amenability of A and φ-splittingof the certain short exact sequence. We show that if S is a weakly cancellative inversesemigroup with subsemigroup ES of idempotents and l1(S) as a Banach module overl1(ES ) is χ-Connes module amenable, then the short exact sequence is χ-splitting that χis a ω∗-continuous bounded module homomorphism from l1(S) onto itself. Other resultsin this direction are also obtained.

On φ-Connes Module Amenability of Dual Banach Algebrasand φ-splitting Keywords:

φ-σwc virtual diagonal , φ-Connes module amenability , φ-splitting , shortexact sequence , semigroup algebra , weakly cancellative semigroup