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

• Autorzy: A. Blanco
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 47L10: Algebras of operators on Banach spaces and other topological linear spaces
• 46B20: Geometry and structure of normed linear spaces
• 16E40: (Co)homology of rings and algebras (e.g. Hochschild, cyclic, dihedral, etc.)
• 46B28: Spaces of operators; tensor products; approximation properties

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2012
• Tom: 213
• Numer: 2
• Strony: 97-131

Daty

wydano

2012

Twórcy

autor

A. Blanco

• Department of Pure Mathematics, Queen's University Belfast, Belfast BT7 1NN, UK

Identyfikatory

DOI

10.4064/sm213-2-1