Abstract
The discussion of amenability properties of dual Banach algebras makes clear that Definition 2.1.11 is not well-suited to deal with every class of Banach algebras: as it ignores the dual space structure of dual Banach algebras, it is too strong to encompass sufficiently many interesting examples. The “right” notion of amenability for dual Banach algebras is Connes-amenability, which takes the additional structure into account.
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Runde, V. (2020). Operator Amenability. In: Amenable Banach Algebras. Springer Monographs in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-0716-0351-2_8
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DOI: https://doi.org/10.1007/978-1-0716-0351-2_8
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