1-amenability of $\mathcal A(X)$ for Banach spaces with 1-unconditional bases

Volume 213 / 2012

A. Blanco Studia Mathematica 213 (2012), 97-131 MSC: Primary 46B20, 46B28, 47L10; Secondary 16E40. DOI: 10.4064/sm213-2-1


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.


  • A. BlancoDepartment of Pure Mathematics
    Queen's University Belfast
    Belfast BT7 1NN, UK

Search for IMPAN publications

Query phrase too short. Type at least 4 characters.

Rewrite code from the image

Reload image

Reload image