Arithmetic separation and Banach-Saks sets

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:394

Article

Kryczka, Andrzej

关键词: Banach-Saks property;    Real interpolation;    Spreading model;   

DOI  :  10.1016/j.jmaa.2012.04.084

来源: Elsevier

【 摘 要 】

We introduce a measure of deviation from the Banach-Saks property for bounded subsets of Banach spaces. The measure is based on the arithmetic separation of a sequence, which is a close counterpart of James' condition of weak noncompactness. We apply this measure to the polygon interpolation method for bounded linear operators on Banach N-tuples. In particular, we show distributions of operators with the Banach-Saks property among the polygon vertices, which imply this property for all interpolated operators. We establish similar results for a measure of deviation from the alternate signs Banach-Saks property. (C) 2012 Elsevier Inc. All rights reserved.

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