ePrints@IIScePrints@IISc Home | About | Browse | Latest Additions | Advanced Search | Contact | Help

On best approximations to compact operators

Sain, D (2021) On best approximations to compact operators. In: Proceedings of the American Mathematical Society, 149 (10). pp. 4273-4286.

pro_ame_mat_soc_149-10_4273-4286_2021.pdf - Published Version

Download (220kB) | Preview
Official URL: https://doi.org/10.1090/PROC/15494


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 lnp 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. © 2021 by Debmalya Sain.

Item Type: Journal Article
Publication: Proceedings of the American Mathematical Society
Publisher: American Mathematical Society
Additional Information: The copyright for this article belongs to Authors
Department/Centre: Division of Physical & Mathematical Sciences > Mathematics
Date Deposited: 02 Dec 2021 12:51
Last Modified: 02 Dec 2021 12:51
URI: http://eprints.iisc.ac.in/id/eprint/70064

Actions (login required)

View Item View Item