Comptes Rendus
Functional Analysis
A weak Hilbert space with few symmetries
[Un espace failble de Hilbert avec peu de symétries]
Comptes Rendus. Mathématique, Volume 348 (2010) no. 23-24, pp. 1293-1296.

Nous construisons un space de Banach Xwh qui est un espace failble de Hilbert et n'admettant aucune sous-espace bloc isomorphe linéaire à une sous-espace. Nous démontrons les propriétés de Xwh par démontrons que Xwh est fortement asymptotique 2 et tout opérateur borné de Xwh soit une variation strictment singulière d'un opérateur diagonal par rappert à la base.

We construct a separable Banach space Xwh with an unconditional basis that is a weak Hilbert space and no block subspace is linearly isomorphic to any of its proper subspaces. We prove that the space Xwh satisfies these properties by showing it is strongly asymptotic 2 and that every bounded linear operator on Xwh is a strictly singular perturbation of a diagonal operator with respect to the unit vector basis.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2010.10.032

Spiros A. Argyros 1 ; Kevin Beanland 2 ; Theocharis Raikoftsalis 1

1 Department of Mathematics, Zografou Campus, National Technical University, Athens 15780, Greece
2 Department of Mathematics and Applied Mathematics, Virginia Commonwealth University, Richmond, VA 23284, United States
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     title = {A weak {Hilbert} space with few symmetries},
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Spiros A. Argyros; Kevin Beanland; Theocharis Raikoftsalis. A weak Hilbert space with few symmetries. Comptes Rendus. Mathématique, Volume 348 (2010) no. 23-24, pp. 1293-1296. doi : 10.1016/j.crma.2010.10.032. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2010.10.032/

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