Approximate ideal connes amenability of dual Banach algebras and ideal connes amenability of discrete Beurling algebras

The concept of approximate Connes amenability of dual Banach algebras was introduced in [9]. In this paper we introduce approximate ideal Connes amenability for dual Banach algebras. We show that every approximate Connes amenable dual Banach algebra is approximate ideally Connes amenable. The notion of ideal Connes amenability for dual Banach algebras was introduced in [14]. In this paper we also study ideal Connes amenability for discrete Beurling algebras.