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