An amalgamation of the Banach spaces associated with James and Schreier, Part I: Banach-space structure
Volume 91 / 2010
Banach Center Publications 91 (2010), 45-76
MSC: Primary 46B45; Secondary 46B03, 47B37.
DOI: 10.4064/bc91-0-3
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.
