On the Norm Attainment Set of a Bounded Linear Operator and Semi-Inner-Products in Normed Spaces

Sain, D (2020) On the Norm Attainment Set of a Bounded Linear Operator and Semi-Inner-Products in Normed Spaces. In: Indian Journal of Pure and Applied Mathematics, 51 (1). pp. 179-186.

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Abstract

We obtain a complete characterization of the norm attainment set of a bounded linear operator between normed spaces, in terms of semi-inner-product(s) defined on the space. In particular, this answers an open question raised recently in D. Sain, On the norm attainment set of a bounded linear operator, J. Math. Anal. Appl., 457 (2018), 67�76. Our results illustrate the applicability of semi-inner-products towards a better understanding of the geometry of normed spaces. © 2020, Indian National Science Academy.

Item Type:	Journal Article
Publication:	Indian Journal of Pure and Applied Mathematics
Publisher:	Indian National Science Academy
Additional Information:	The copyright of this article belongs to Indian National Science Academy
Department/Centre:	Division of Physical & Mathematical Sciences > Mathematics
Date Deposited:	01 Jul 2020 09:53
Last Modified:	01 Jul 2020 09:53
URI:	http://eprints.iisc.ac.in/id/eprint/64956

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