φ-connes module amenability of dual banach algebras and φ-splitting

In this talk, we dene ö-connes module amenability of a dualbanach algebra a, where ö is a !-continuous bounded module homomor-phism from a onto itself. we obtain the relation between ö-connes moduleamenability of a and ö-splitting of the certain short exact sequence. weshow that if s is a weakly cancellative inverse semigroup with subsemigroupes of idempotents and l1(s) as a banach module over l1(es) is -connesmodule amenable, then the short exact sequence is -splitting that  is a!-continuous bounded module homomorphism from l1(s) onto itself.