Journal
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
Volume 509, Issue 1, Pages -Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jmaa.2021.125952
Keywords
Best approximation; Distance formulae; orthogonality; Linear operators; Banach space
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Funding
- [MTR/2017/000059]
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In this paper, several distance formulae in the space of compact operators are presented in terms of extreme points and semi-inner-products. The best approximation to an element out of a subspace is characterized, and a sufficient condition for unique best approximation is obtained. The usefulness of the results is demonstrated with examples. Finally, using the distance formulae, the approximate Birkhoff-James orthogonality of an element to a subspace in the space of compact operators is characterized.
We present several distance formulae in the space of compact operators in terms of extreme points and semi-inner-products. We characterize best approximation to an element out of a subspace and obtain a sufficient condition for unique best approximation. The usefulness of the results is demonstrated with examples. Finally, using the distance formulae we characterize approximate Birkhoff-James orthogonality of an element to a subspace in the space of compact operators.(c) 2021 Elsevier Inc. All rights reserved.
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