Distance formulae and best approximation in the space of compact operators

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Distance formulae and best approximation in the space of compact operators

Mal, Arpita; Paul, Kallol

Journal of mathematical analysis and applications, 05/2022, Volume: 509, Issue: 1

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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.

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