2021/04/28 by Debmalya Sain, Sain, Debmalya · 2 citations
Computer Science · Mathematics · #Advanced Banach Space Theory #Approximation Theory and Sequence Spaces #FOS: Mathematics #Functional Analysis (math.FA) #Optimization and Variational Analysis #Primary 46B28 #Secondary 46B20
paper · pdf · doi:10.48550/arxiv.2104.13975
openalex publication_date 2021/04/28 · openalex created_date 2021/05/10 · openalex updated_date 2026/07/28
We study best approximations to compact operators between Banach spaces and Hilbert spaces, from the point of view of Birkhoff-James orthogonality and semi-inner-products. As an application of the present study, some distance formulae are presented in the space of compact operators. The special case of bounded linear functionals as compact operators is treated separately and some applications to best approximations in reflexive, strictly convex and smooth Banach spaces are discussed. An explicit example is presented in ℓpn spaces, where 1 < p < ∞, to illustrate the applicability of the methods developed in this article. A comparative analysis of the results presented in this article with the well-known classical duality principle in approximation theory is conducted to demonstrate the advantage in the former case, from a computational point of view.