Haar negligibility of positive cones in Banach spaces
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- by J. Esterle, É. Matheron and P. Moreau
- St. Petersburg Math. J. 27 (2016), 731-756
- DOI: https://doi.org/10.1090/spmj/1414
- Published electronically: July 26, 2016
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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.References
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Bibliographic Information
- J. Esterle
- Affiliation: IMB, UMR 5251, Université de Bordeaux, 351 cours de la Libération, 33405 Talence, France
- MR Author ID: 64315
- Email: esterle@math.u-bordeaux1.fr
- É. Matheron
- Affiliation: Laboratoire de Mathématiques de Lens, Université d’Artois, 18 Rue Jean Souvraz S. P., 62307 Lens, France
- MR Author ID: 348460
- Email: etienne.matheron@euler.univ-artois.fr
- P. Moreau
- Affiliation: Lycée La Pérouse-Kerichen, Rue Prince de Joinville - BP 82517, 29225 Brest cedex 2, France
- Email: pierre.moreau@ac-rennes.fr
- Received by editor(s): April 6, 2015
- Published electronically: July 26, 2016
- © Copyright 2016 American Mathematical Society
- Journal: St. Petersburg Math. J. 27 (2016), 731-756
- MSC (2010): Primary 46B25
- DOI: https://doi.org/10.1090/spmj/1414
- MathSciNet review: 3582941