Approximate injectivity of dual Banach algebras

Abstract

A new notion of injectivity is introduced. It is shown that approximate Connes-amenability and approximate injectivity are the same properties. As a consequence, approximate Connes-amenability of the direct sum of dual Banach algebras is discussed. A characterization is given for approximate Connes-amenability of dual Banach algebras in terms of the approximate splitting of certain short exact sequence.