The approximation properties determined by operator ideals

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• 作者：Dong Yang Chen ; Lei Li
• 关键词：Approximation property ; operator ideals ; bounded approximation property ; A ; p ; compact sets
• 刊名：Acta Mathematica Sinica, English Series
• 出版年：2017
• 出版时间：March 2017
• 年：2017
• 卷：33
• 期：3
• 页码：311-326
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics, general;
• 出版者：Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society
• ISSN：1439-7617
• 卷排序：33

文摘

We introduce the notion of the right approximation property with respect to an operator ideal A and solve the duality problem for the approximation property with respect to an operator ideal A, that is, a Banach space X has the approximation property with respect to Ad whenever X* has the right approximation property with respect to an operator ideal A. The notions of the left bounded approximation property and the left weak bounded approximation property for a Banach operator ideal are introduced and new symmetric results are obtained. Finally, the notions of the p-compact sets and the p-approximation property are extended to arbitrary Banach operator ideals. Known results of the approximation property with respect to an operator ideal and the p-approximation property are generalized.