Some geometric properties of finite dimensional, symmetric Banach spaces

C. Schütt

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A Banach space with a symmetric basis which contains no $ℓ_{p}$ or $c_{0}$ , and all its symmetric basic sequences are equivalent

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The main result of the note is a characterization of 1-amenability of Banach algebras of approximable operators for a class of Banach spaces with 1-unconditional bases in terms of a new basis property. It is also shown that amenability and symmetric amenability are equivalent concepts for Banach algebras of approximable operators, and that a type of Banach space that was long suspected to lack property 𝔸 has in fact the property. Some further ideas on the problem of whether or not amenability...

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