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 l۱(S) as a Banach module overl۱(ES ) is χ-Connes module amenable, then the short exact sequence is χ-splitting that χis a ω∗-continuous bounded module homomorphism from l۱(S) onto itself. Other resultsin this direction are also obtained.

کلیدواژه ها:

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