Distance formulae and best approximation in the space of compact operators

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.

Automated summary

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.