Approximate Connes-amenability of dual Banach algebras

作者：Esslamzadeh G H; Shojaee B^*; Mahmoodi A

来源：Bulletin of the Belgian Mathematical Society Simon Stevin, 2012, 19(2): 193-213.

• Approximately inner derivation
• Approximately Connes amenable
• Approximately strongly Connes amenable
• Approximate normal virtual diagonal
• Approximate sigma WC-virtual diagonal

We introduce the notions of approximate Connes-amenability and approximate strong Connes-amenability for dual Banach algebras. Then we characterize these two types of algebras in terms of approximate normal virtual diagonals and approximate sigma WC-virtual diagonals. We investigate these properties for von Neumann algebras, measure algebra and the algebra of p-pseudomeasures on locally compact groups. In particular we show that a von Neumann algebra is approximately Connes-amenable if and only if it has an approximate normal virtual diagonal. This is the %26quot;approximate%26quot; analog of the main result of Effros in [10]. %26lt;br%26gt;We show that in general the concepts of approximate Connes-amenability and Connes-amenability are distinct, but for measure algebras these two concepts coincide. Moreover cases where approximate Connes-amenability of A** implies approximate Connes-amenability or approximate amenability of A are also discussed.

• 出版日期2012-7