On Approximate Ideal Amenability in Banach Algebras

Abstract

The notions of approximate I-weak amenability and approximate ideal amenability in Banach algebras are introduced. General theory is developed for these notions, and in particular, we show that the approximate ideal amenability of the Segal algebra S(G) in L(G) implies that G, and hence L(G) is amenable. Mathematics Subject Classification 2000: 46H20, 46H10, 46H25.