Some remarks on James–Schreier spaces

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• 作者：Alistair Bird ; Niels Jakob Laustsen ; Andrá ; s Zsá ; k
• 关键词：Banach space ; James– ; Schreier space ; Schreier space ; Shrinking Schauder basis ; Peł ; czyń ; ski's property (u)
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2010
• 出版时间：15 November 2010
• 年：2010
• 卷：371
• 期：2
• 页码：609-613
• 全文大小：154 K

文摘

The James–Schreier spaces V_p, where 1p<∞, were recently introduced by Bird and Laustsen (in press) [5] 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 in Bird and Laustsen (in press) [5]. Specifically, we prove that (i) the standard Schauder basis for the first James–Schreier space V₁ is shrinking, and (ii) any two Schreier or James–Schreier spaces with distinct indices are non-isomorphic. The former of these results implies that V₁ does not have Pełczyński's property (u) and hence does not embed in any Banach space with an unconditional Schauder basis.