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ON TWO EXTREMUM PROBLEMS RELATED TO THE NORM OF A BOUNDED LINEAR OPERATOR

Sain, Debmalya and Paul, Kallol and Mandal, Kalidas (2019) ON TWO EXTREMUM PROBLEMS RELATED TO THE NORM OF A BOUNDED LINEAR OPERATOR. In: OPERATORS AND MATRICES, 13 (2). pp. 421-432.

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Official URL: https://dx.doi.org/10.7153/oam-2019-13-31

Abstract

We explore the norm attainment set and the minimum norm attainment set of a bounded linear operator between Hilbert spaces and Banach spaces. Indeed, we obtain a complete characterization of both the sets, separately for operators between Hilbert spaces and Banach spaces. We also study the interconnection between these two sets and prove that for operators between Hilbert spaces, these two sets are either equal or mutually orthogonal, provided both of them are non-empty. We also obtain separate complete characterizations of reflexive Banach spaces and Euclidean spaces in terms of the norm (minimum norm) attainment set, in order to illustrate the importance of our study.

Item Type: Journal Article
Additional Information: copyright for this article belongs to ELEMENT
Keywords: Orthogonality; linear operators; norm attainment
Department/Centre: Division of Physical & Mathematical Sciences > Mathematics
Depositing User: Id for Latest eprints
Date Deposited: 04 Sep 2019 10:00
Last Modified: 05 Sep 2019 06:16
URI: http://eprints.iisc.ac.in/id/eprint/63469

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