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St. Petersburg Mathematical Journal

ISSN 1547-7371(online) ISSN 1061-0022(print)



Haar negligibility of positive cones in Banach spaces

Authors: J. Esterle, É. Matheron and P. Moreau
Original publication: Algebra i Analiz, tom 27 (2015), nomer 5.
Journal: St. Petersburg Math. J. 27 (2016), 731-756
MSC (2010): Primary 46B25
Published electronically: July 26, 2016
MathSciNet review: 3582941
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Abstract: The Haar negligibility of the positive cone associated with a basic sequence is discussed in the case of a separable Banach space. In particular, it is shown that, up to equivalence, the canonical basis of $c_0$ is the only normalized subsymmetric unconditional basic sequence whose positive cone is not Haar null, and the only normalized unconditional basic sequence whose positive cone contains a translate of every compact set. It is also proved that an unconditional basic sequence with a non-Haar null positive cone must be $c_0$-saturated in a very strong sense, and that every quotient of the space generated by such a sequence is $c_0$-saturated.

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Additional Information

J. Esterle
Affiliation: IMB, UMR 5251, Université de Bordeaux, 351 cours de la Libération, 33405 Talence, France
MR Author ID: 64315

É. Matheron
Affiliation: Laboratoire de Mathématiques de Lens, Université d’Artois, 18 Rue Jean Souvraz S. P., 62307 Lens, France
MR Author ID: 348460

P. Moreau
Affiliation: Lycée La Pérouse-Kerichen, Rue Prince de Joinville - BP 82517, 29225 Brest cedex 2, France

Keywords: Haar negligibility, positive cone, Schauder base, Gauss negligibility
Received by editor(s): April 6, 2015
Published electronically: July 26, 2016
Article copyright: © Copyright 2016 American Mathematical Society