☆ 4.5 Article

Distance formulae and best approximation in the space of compact operators

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS (2022)

ON BEST APPROXIMATIONS TO COMPACT OPERATORS

Debmalya Sain

Summary: This study examines best approximations to compact operators between Banach spaces and Hilbert spaces, focusing on Birkhoff-James orthogonality and semi-inner products. Distance formulas in the space of compact operators are presented as an application of the study. Specific applications to reflexive, strictly convex, and smooth Banach spaces are discussed, with an explicit example in l(p)(n) spaces demonstrating the applicability of the methods developed. A comparative analysis with the classical duality principle in approximation theory shows the computational advantage of the methods proposed in this article.

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY (2021)

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Article Mathematics

BIRKHOFF-JAMES ORTHOGONALITY TO A SUBSPACE OF OPERATORS DEFINED BETWEEN BANACH SPACES

Arpita Mal et al.

Summary: This paper examines the Birkhoff-James orthogonality of a linear operator to a subspace of operators defined between arbitrary Banach spaces. The study provides a complete characterization when the domain space is reflexive and the subspace is finite dimensional, as well as under additional conditions for arbitrary Banach spaces. It also explores orthogonality to a subspace of the space of linear operators in an arbitrary Hilbert space, considering both operator norm and numerical radius norm.

JOURNAL OF OPERATOR THEORY (2021)

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Article Mathematics