Geodesic
1-amenability of $\mathcal A(X)$ for Banach spaces with 1-unconditional bases
A. Blanco1
1 Department of Pure Mathematics Queen's University Belfast Belfast BT7 1NN, UK
Studia Mathematica, Tome 213 (2012) no. 2, pp. 97-131

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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 $\mathbb A$ has in fact the property. Some further ideas on the problem of whether or not amenability (in this setting) implies property $\mathbb A$ are discussed.
DOI : 10.4064/sm213-2-1
Keywords: main result note characterization amenability banach algebras approximable operators class banach spaces unconditional bases terms basis property shown amenability symmetric amenability equivalent concepts banach algebras approximable operators type banach space long suspected lack property mathbb has property further ideas problem whether amenability setting implies property mathbb discussed

A. Blanco 1

1 Department of Pure Mathematics Queen's University Belfast Belfast BT7 1NN, UK 
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A. Blanco. 1-amenability of $\mathcal A(X)$ for Banach spaces  with
1-unconditional bases. Studia Mathematica, Tome 213 (2012) no. 2, pp. 97-131. doi: 10.4064/sm213-2-1

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