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.
"Approximate injectivity of dual Banach algebras." Bull. Belg. Math. Soc. Simon Stevin 20 (5) 831 - 842, november 2013. https://doi.org/10.36045/bbms/1385390767