Ideal Connes-Amenability of Dual Banach Algebras

A new class of ideal Connes amenability

“…It is easy to see that A does not have bounded approximate identity. So A is not ideally Connes amenable [7].…”

“…On the other hand, multiplication in A and A I is separately weak * -continuous and thus A I is a dual Banach algebra. For details on this and other important results, refer to [5,8,10,11] and the references therein.…”

“…He proved that the operator C * −algebra A is Connes amenable if and only if the Banach A−bimodule Ā * is injective. The first author, Bodaghi and Ebrahimi Bagha [7] generalized the concept of Connes amenability and introduced the notion of ideally Connes amenability for dual Banach algebras. They proved that von Neumann algebras are ideally Connes amenable; see also [12]; for study of the notion of quotient ideal amenability of Banach algebras see [16].…”

“…and is ideally Connes amenable if it is I-Connes amenable for every weak * -closed two-sided ideal I in A; see [7]. Note that I is a dual Banach space with predual I * = A * ⊥ I .…”

A generalization on character Connes-amenability

“…They characterized the structure of approximately amenable Banach algebras through several different ways. After that, this notion was generalized for dual Banach algebras, namely, approximate Connes-amenability [8] and ideal Connes-amenability [15].…”