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An amalgamation of the Banach spaces associated with James and Schreier, Part I : Banach-space structure.

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An amalgamation of the Banach spaces associated with James and Schreier, Part I : Banach-space structure. / Bird, Alistair; Laustsen, Niels Jakob.
In: Banach Center Publications, Vol. 91, 12.2010, p. 45-76.

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

Harvard

Bird, A & Laustsen, NJ 2010, 'An amalgamation of the Banach spaces associated with James and Schreier, Part I : Banach-space structure.', Banach Center Publications, vol. 91, pp. 45-76. https://doi.org/10.4064/bc91-0-3

APA

Bird, A., & Laustsen, N. J. (2010). An amalgamation of the Banach spaces associated with James and Schreier, Part I : Banach-space structure. Banach Center Publications, 91, 45-76. https://doi.org/10.4064/bc91-0-3

Vancouver

Bird A, Laustsen NJ. An amalgamation of the Banach spaces associated with James and Schreier, Part I : Banach-space structure. Banach Center Publications. 2010 Dec;91:45-76. doi: 10.4064/bc91-0-3

Author

Bird, Alistair ; Laustsen, Niels Jakob. / An amalgamation of the Banach spaces associated with James and Schreier, Part I : Banach-space structure. In: Banach Center Publications. 2010 ; Vol. 91. pp. 45-76.

Bibtex

@article{51f8e301b5a042fcb416383d09975c5f,
title = "An amalgamation of the Banach spaces associated with James and Schreier, Part I : Banach-space structure.",
abstract = "We create a new family of Banach spaces, the James-Schreier spaces, by amalgamating two important classical Banach spaces: 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. We then investigate the properties of these James-Schreier spaces, paying particular attention to how key properties of their `ancestors' (that is, the James space and the Schreier space) are expressed in them. Our main results include that each James-Schreier space is c_0-saturated and that no James-Schreier space embeds in a Banach space with an unconditional basis.",
keywords = "Banach space, James space, Schreier space, shrinking basis, shift operator, c_0-saturation, Pelczynski's property (u).",
author = "Alistair Bird and Laustsen, {Niels Jakob}",
note = "2010 Mathematics Subject Classification: Primary 46B45; Secondary 46B03, 47B37.",
year = "2010",
month = dec,
doi = "10.4064/bc91-0-3",
language = "English",
volume = "91",
pages = "45--76",
journal = "Banach Center Publications",
issn = "0137-6934",

}

RIS

TY - JOUR

T1 - An amalgamation of the Banach spaces associated with James and Schreier, Part I : Banach-space structure.

AU - Bird, Alistair

AU - Laustsen, Niels Jakob

N1 - 2010 Mathematics Subject Classification: Primary 46B45; Secondary 46B03, 47B37.

PY - 2010/12

Y1 - 2010/12

N2 - We create a new family of Banach spaces, the James-Schreier spaces, by amalgamating two important classical Banach spaces: 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. We then investigate the properties of these James-Schreier spaces, paying particular attention to how key properties of their `ancestors' (that is, the James space and the Schreier space) are expressed in them. Our main results include that each James-Schreier space is c_0-saturated and that no James-Schreier space embeds in a Banach space with an unconditional basis.

AB - We create a new family of Banach spaces, the James-Schreier spaces, by amalgamating two important classical Banach spaces: 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. We then investigate the properties of these James-Schreier spaces, paying particular attention to how key properties of their `ancestors' (that is, the James space and the Schreier space) are expressed in them. Our main results include that each James-Schreier space is c_0-saturated and that no James-Schreier space embeds in a Banach space with an unconditional basis.

KW - Banach space

KW - James space

KW - Schreier space

KW - shrinking basis

KW - shift operator

KW - c_0-saturation

KW - Pelczynski's property (u).

U2 - 10.4064/bc91-0-3

DO - 10.4064/bc91-0-3

M3 - Journal article

VL - 91

SP - 45

EP - 76

JO - Banach Center Publications

JF - Banach Center Publications

SN - 0137-6934

ER -