Amenability and Contractibility Modulo an Ideal of Banach Algebras

Abstract

We investigate the concept of amenability modulo an ideal of Banach algebra, showing that amenability modulo an ideal can be characterized by the existence of virtual and approximate diagonal modulo an ideal. We also study the concept of contractible modulo an ideal of Banach algebra. As a consequence, we prove a version of Selivanov's theorem for a large class of semigroups, including E-inversive E-semigroup and eventually inverse semigroups.