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Some remarks on James-Schreier spaces.

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Some remarks on James-Schreier spaces. / Bird, Alistair; Laustsen, Niels Jakob; Zsak, Andras.
In: Journal of Mathematical Analysis and Applications, Vol. 371, No. 2, 15.11.2010, p. 609-613.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Harvard

Bird, A, Laustsen, NJ & Zsak, A 2010, 'Some remarks on James-Schreier spaces.', Journal of Mathematical Analysis and Applications, vol. 371, no. 2, pp. 609-613. https://doi.org/10.1016/j.jmaa.2010.05.067

APA

Bird, A., Laustsen, N. J., & Zsak, A. (2010). Some remarks on James-Schreier spaces. Journal of Mathematical Analysis and Applications, 371(2), 609-613. https://doi.org/10.1016/j.jmaa.2010.05.067

Vancouver

Bird A, Laustsen NJ, Zsak A. Some remarks on James-Schreier spaces. Journal of Mathematical Analysis and Applications. 2010 Nov 15;371(2):609-613. doi: 10.1016/j.jmaa.2010.05.067

Author

Bird, Alistair ; Laustsen, Niels Jakob ; Zsak, Andras. / Some remarks on James-Schreier spaces. In: Journal of Mathematical Analysis and Applications. 2010 ; Vol. 371, No. 2. pp. 609-613.

Bibtex

@article{d3cbaf8a283b4b44b2db87e6977de733,
title = "Some remarks on James-Schreier spaces.",
abstract = "The James-Schreier spaces V_p, where p is a real number greater than or equal to 1, were recently introduced by Bird and Laustsen as an amalgamation of James' quasi-reflexive Banach space on the one hand and Schreier's Banach space giving a counterexample to the Banach-Saks property on the other. The purpose of this note is to answer some questions left open by Bird and Laustsen. Specifically, we prove that (i) the standard Schauder basis for the first James-Schreier space V_1 is shrinking, and (ii) any two Schreier or James-Schreier spaces with distinct indices are non-isomorphic. The former of these results implies that V_1 does not have Pelczynski's property (u) and hence does not embed in any Banach space with an unconditional Schauder basis.",
keywords = "Banach space, James-Schreier space, Schreier space, shrinking Schauder basis, Pelczynski's property (u)",
author = "Alistair Bird and Laustsen, {Niels Jakob} and Andras Zsak",
note = "2000 Mathematics Subject Classification: primary 46B03, 46B45; secondary 46B15. The final, definitive version of this article has been published in the Journal, Journal of Mathematical Analysis and Applications 371 (2), 2010, {\textcopyright} ELSEVIER.",
year = "2010",
month = nov,
day = "15",
doi = "10.1016/j.jmaa.2010.05.067",
language = "English",
volume = "371",
pages = "609--613",
journal = "Journal of Mathematical Analysis and Applications",
issn = "0022-247X",
publisher = "Academic Press Inc.",
number = "2",

}

RIS

TY - JOUR

T1 - Some remarks on James-Schreier spaces.

AU - Bird, Alistair

AU - Laustsen, Niels Jakob

AU - Zsak, Andras

N1 - 2000 Mathematics Subject Classification: primary 46B03, 46B45; secondary 46B15. The final, definitive version of this article has been published in the Journal, Journal of Mathematical Analysis and Applications 371 (2), 2010, © ELSEVIER.

PY - 2010/11/15

Y1 - 2010/11/15

N2 - The James-Schreier spaces V_p, where p is a real number greater than or equal to 1, were recently introduced by Bird and Laustsen as an amalgamation of James' quasi-reflexive Banach space on the one hand and Schreier's Banach space giving a counterexample to the Banach-Saks property on the other. The purpose of this note is to answer some questions left open by Bird and Laustsen. Specifically, we prove that (i) the standard Schauder basis for the first James-Schreier space V_1 is shrinking, and (ii) any two Schreier or James-Schreier spaces with distinct indices are non-isomorphic. The former of these results implies that V_1 does not have Pelczynski's property (u) and hence does not embed in any Banach space with an unconditional Schauder basis.

AB - The James-Schreier spaces V_p, where p is a real number greater than or equal to 1, were recently introduced by Bird and Laustsen as an amalgamation of James' quasi-reflexive Banach space on the one hand and Schreier's Banach space giving a counterexample to the Banach-Saks property on the other. The purpose of this note is to answer some questions left open by Bird and Laustsen. Specifically, we prove that (i) the standard Schauder basis for the first James-Schreier space V_1 is shrinking, and (ii) any two Schreier or James-Schreier spaces with distinct indices are non-isomorphic. The former of these results implies that V_1 does not have Pelczynski's property (u) and hence does not embed in any Banach space with an unconditional Schauder basis.

KW - Banach space

KW - James-Schreier space

KW - Schreier space

KW - shrinking Schauder basis

KW - Pelczynski's property (u)

U2 - 10.1016/j.jmaa.2010.05.067

DO - 10.1016/j.jmaa.2010.05.067

M3 - Journal article

VL - 371

SP - 609

EP - 613

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

SN - 0022-247X

IS - 2

ER -