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In the first part of this work, we establish some general properties of dual algebras and of direct integral dual algebras. In the second part, we give a complete description of singly generated uniform dual algebras of operators.
We introduce and study the notions of w*-approximate Connes amenability and pseudo-Connes amenability for dual Banach algebras. We prove that the dual Banach sequence algebra ℓ¹ is not w*-approximately Connes amenable. We show that in general the concepts of pseudo-Connes amenability and Connes amenability are distinct. Moreover the relations between these new notions are also discussed.
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