A weak Hilbert space with few symmetries

Argyros, Spiros A.; Beanland, Kevin; Raikoftsalis, Theocharis

doi:10.1016/j.crma.2010.10.032

Functional Analysis

A weak Hilbert space with few symmetries
[Un espace failble de Hilbert avec peu de symétries]

Présenté par : Gilles Pisier

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

Comptes Rendus. Mathématique, Tome 348 (2010) no. 23-24, pp. 1293-1296.

Résumé
Abstract

Nous construisons un space de Banach $X_{w h}$ 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 $X_{w h}$ par démontrons que $X_{w h}$ est fortement asymptotique $ℓ_{2}$ et tout opérateur borné de $X_{w h}$ soit une variation strictment singulière d'un opérateur diagonal par rappert à la base.

We construct a separable Banach space $X_{w h}$ 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 $X_{w h}$ satisfies these properties by showing it is strongly asymptotic $ℓ_{2}$ and that every bounded linear operator on $X_{w h}$ is a strictly singular perturbation of a diagonal operator with respect to the unit vector basis.

Reçu le : 2010-09-08
Accepté le : 2010-10-25
Publié le : 2010-11-18

DOI : 10.1016/j.crma.2010.10.032

Affiliations des auteurs :

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

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     title = {A weak {Hilbert} space with few symmetries},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {1293--1296},
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Argyros, Spiros A.; Beanland, Kevin; Raikoftsalis, Theocharis. A weak Hilbert space with few symmetries. Comptes Rendus. Mathématique, Tome 348 (2010) no. 23-24, pp. 1293-1296. doi : 10.1016/j.crma.2010.10.032. http://www.numdam.org/articles/10.1016/j.crma.2010.10.032/

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