Skip to Main Content

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

On best approximations to compact operators
HTML articles powered by AMS MathViewer

by Debmalya Sain PDF
Proc. Amer. Math. Soc. 149 (2021), 4273-4286

Abstract:

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 $\ell _p^{n}$ spaces, where $1 < p < \infty ,$ 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.
References
Similar Articles
  • Retrieve articles in Proceedings of the American Mathematical Society with MSC (2020): 46B28, 46B20
  • Retrieve articles in all journals with MSC (2020): 46B28, 46B20
Additional Information
  • Debmalya Sain
  • Affiliation: Department of Mathematics, Indian Institute of Science, Bengaluru 560012, Karnataka, India
  • MR Author ID: 1024072
  • ORCID: 0000-0002-9721-1597
  • Email: saindebmalya@gmail.com
  • Received by editor(s): October 14, 2020
  • Received by editor(s) in revised form: January 1, 2021
  • Published electronically: July 21, 2021
  • Communicated by: Javad Mashreghi
  • © Copyright 2021 by Debmalya Sain
  • Journal: Proc. Amer. Math. Soc. 149 (2021), 4273-4286
  • MSC (2020): Primary 46B28; Secondary 46B20
  • DOI: https://doi.org/10.1090/proc/15494
  • MathSciNet review: 4305980