Ideal Connes-Amenability of Dual Banach Algebras

Following Runde, we define the concept of ideal Connes-amenability for dual Banach algebras. For an Arens regular dual Banach algebra A, we prove that the ideal Connes-amenability of A**, the second dual of A necessities ideal Connes-amenability of A. As a typical example, we show that von Neumann algebras are always ideally Connes-amenable. For a locally compact group G, the Fourier-Stieltjes algebra of G is ideally Connes-amenable, but not ideally amenable.