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Comptes Rendus MathematiqueVolume 337, Issue 1, 1 July 2003, Pages 43-48

A class of Banach spaces with no unconditional basic sequence(Article)(Open Access)

[Une classe d'espace de Banach sans suite basique inconditionnelle]

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  • aDepartment of Mathematics, National Technical Univ. of Athens, Zogratou Campus, 15780 Athens, Greece
  • bEquipe de Logique Mathematique, Université Paris VII, 2 place Jussieu, 75251 Paris Cedex, France
  • cCNRS-Université Paris VII, 2 place Jussieu, 75251 Paris Cedex, France

Abstract

We give a construction of a reflexive Banach space Xω1 with a transfinite basis of length ω1 and with no unconditional basic sequence. In addition every bounded operator from a subspace of Xω1 into the space Xω1 is a sum of a simple diagonal operator and a strictly singular one. © 2003 Académie des sciences. Published by Éditions scientifiques et médicales Elsevier SAS. All rights reserved.

  • ISSN: 1631073X
  • Source Type: Journal
  • Original language: English, French
  • DOI: 10.1016/S1631-073X(03)00272-3
  • Document Type: Article
  • Publisher: Elsevier Masson SAS

  Argyros, S.A.; Department of Mathematics, Natl. Technical University of Athens, Zogratou Campus, Greece;
© Copyright 2017 Elsevier B.V., All rights reserved.

Cited by 8 documents

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Strictly singular non-compact diagonal operators on HI spaces
(2010) Houston Journal of Mathematics
Koszmider, P.
A survey on Banach spaces C(K) with few operators | Una revisíon de los espacios de Banach C(K) con pocos operadores
(2010) Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales - Serie A: Matematicas
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