非阿基米德赋范空间之间的类紧算子

Indagationes Mathematicae (Proceedings) Pub Date : 1989-01-01 DOI:10.1016/1385-7258(89)90005-X

N. de Grande-de Kimpe , J. Martinez-Maurica

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引用次数: 3

摘要

最近由W. Schikhof提出的关于非阿基米德巴拿赫空间E上紧算子的Fredholm理论，如果放弃E的完备性假设，则不起作用。这使得作者在非阿基米德赋范空间中引入了两个新的算子理想，在巴拿赫空间中它们与紧算子的理想重合。他们还以不同的方式研究了三个算子理想可能的相等性。

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Compact-like operators between non-archimedean normed spaces

The Fredholm theory for compact operators on a non-archimedean Banach space E, as recently developed by W. Schikhof, does not work if the hypothesis of the completeness of E is dropped. This observation led the authors to introduce two new ideals of operators between non-archimedean normed spaces which, in the case of Banach spaces coincide with the ideal of the compact operators. They also investigate in various ways the possible equality of the three operator ideals.

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Indagationes Mathematicae (Proceedings)

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