1-amenability of $\mathcal A(X)$ for Banach spaces with
1-unconditional bases
Studia Mathematica, Tome 213 (2012) no. 2, pp. 97-131
Cet article a éte moissonné depuis 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.
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
Affiliations des auteurs :
A. Blanco 1
@article{10_4064_sm213_2_1,
author = {A. Blanco},
title = {1-amenability of $\mathcal A(X)$ for {Banach} spaces with
1-unconditional bases},
journal = {Studia Mathematica},
pages = {97--131},
year = {2012},
volume = {213},
number = {2},
doi = {10.4064/sm213-2-1},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/sm213-2-1/}
}
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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