Arithmetic separation and Banach-Saks sets

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• 作者：Andrzej Kryczka ^{andrzej.kryczka@umcs.pl}
• 关键词：Banach&ndash ; Saks property ; Real interpolation ; Spreading model
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2012
• 期刊代码：76_0022247x
• 类别：mt
• 出版时间：15 October, 2012
• 卷：394
• 期：2
• 页码：772-780
• 文件大小：247 K

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鈥?condition of weak noncompactness. We apply this measure to the polygon interpolation method for bounded linear operators on Banach -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.