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