Abstract: In this survey, we first study dual Banach algebras and completely contractive dual Banach algebras. Then, we discuss the Connes-amenability and operator Connes-amenability of these algebras and present some new advances in this area.
Keywords: Locally compact groups; Amenability; Operator spaces; Fourier algebra
Classification (MSC2000): 22D05; 43A07, 47L25
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