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 c0-saturated and that no James‐Schreier space embeds in a Banach space with an unconditional basis. 2010 Mathematics Subject Classification: Primary 46B45; Secondary 46B03, 47B37.
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