Banach-Steinhaus theory revisited: Lineability and spaceability

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• 作者：Holger Boche ^boche@tum.de ; Ullrich J. Mö ; nich ; ^{moenich@tum.de}
• 关键词：46E15 ; 30E05 ; 30E10
• 刊名：Journal of Approximation Theory
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：213
• 期：Complete
• 页码：50-69
• 全文大小：296 K
• 卷排序：213

文摘

In this paper we study the divergence behavior of linear approximation processes in general Banach spaces. We are interested in the structure of the set of vectors creating divergence. The Banach–Steinhaus theory gives some information about this set, however, it cannot be used to answer the question whether this set contains subspaces with linear structure. We give necessary and sufficient conditions for the lineability and the spaceability of the set of vectors creating divergence.