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 (in this setting) implies property 𝔸 are discussed.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm213-2-1,
author = {A. Blanco},
title = {1-amenability of A(X) for Banach spaces with 1-unconditional bases},
journal = {Studia Mathematica},
volume = {209},
year = {2012},
pages = {97-131},
zbl = {1303.46017},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm213-2-1}
}
A. Blanco. 1-amenability of 𝒜(X) for Banach spaces with 1-unconditional bases. Studia Mathematica, Tome 209 (2012) pp. 97-131. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm213-2-1/