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 c₀-saturated and that no James-Schreier space embeds in a Banach space with an unconditional basis.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc91-0-3,
author = {Alistair Bird and Niels Jakob Laustsen},
title = {An amalgamation of the Banach spaces associated with James and Schreier, Part I: Banach-space structure},
journal = {Banach Center Publications},
volume = {89},
year = {2010},
pages = {45-76},
zbl = {1211.46018},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc91-0-3}
}
Alistair Bird; Niels Jakob Laustsen. An amalgamation of the Banach spaces associated with James and Schreier, Part I: Banach-space structure. Banach Center Publications, Tome 89 (2010) pp. 45-76. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc91-0-3/