Best approximation in spaces of compact operators
Let K(X,Y) be the space of compact operators. For a proximinal subspace Z⊂Y, this paper deals with the question, when does every Y-valued compact operator admit a Z-valued compact best approximation? For any reflexive Banach space X and for a L1-predual space Y, if Z⊂Y is a strongly proximinal subsp...
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Published in | Linear algebra and its applications Vol. 627; pp. 72 - 79 |
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Main Author | |
Format | Journal Article |
Language | English |
Published |
Amsterdam
Elsevier Inc
15.10.2021
American Elsevier Company, Inc |
Subjects | |
Online Access | Get full text |
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Summary: | Let K(X,Y) be the space of compact operators. For a proximinal subspace Z⊂Y, this paper deals with the question, when does every Y-valued compact operator admit a Z-valued compact best approximation? For any reflexive Banach space X and for a L1-predual space Y, if Z⊂Y is a strongly proximinal subspace of finite codimension, we show that K(X,Z) is a proximinal subspace of K(X,Y) under an additional condition on the position of K(X,Z). When Y is a c0-direct sum of finite dimensional spaces we achieve a strong transitivity result by showing that for any proximinal subspace of finite codimension Z⊂Y, every Y-valued bounded operator admits a best Z-valued compact approximation. |
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ISSN: | 0024-3795 1873-1856 |
DOI: | 10.1016/j.laa.2021.06.006 |