Ideal Connes-Amenability of Dual Banach Algebras

Abstract

Following Runde, we define the concept of ideal Connes-amenability for dual Banach algebras. For an Arens regular dual Banach algebra $${\mathcal {A}}$$ , we prove that the ideal Connes-amenability of $$\mathcal {A^{**}}$$ , the second dual of $${\mathcal {A}}$$ necessities ideal Connes-amenability of $${{\mathcal {A}}}$$ . 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.