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On the norm attainment set of a bounded linear operator

Sain, Debmalya (2017) On the norm attainment set of a bounded linear operator. In: JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 457 (1). pp. 67-76.

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Official URL: http://doi.org/10.1016/j.jmaa.2017.07.070

Abstract

In this paper we explore the properties of a bounded linear operator defined on a Banach space, in light of operator norm attainment. Using Birkhoff-James orthogonality techniques, we give a necessary condition for a nonzero bounded linear operator to attain norm at a particular point of the unit sphere. We prove four corollaries to establish the importance of our study. As part of our exploration, we also obtain a characterization of smooth Banach spaces in terms of operator norm attainment and Birkhoff-James orthogonality. Restricting our attention to l(p)(2)(p is an element of N backslash {1}) spaces, we obtain an upper bound for the number of points at which any linear operator, which is not a scalar multiple of an isometry, may attain norm. (c) 2017 Elsevier Inc. All rights reserved.

Item Type: Journal Article
Additional Information: Copy right for this article belongs to the ACADEMIC PRESS INC ELSEVIER SCIENCE, 525 B ST, STE 1900, SAN DIEGO, CA 92101-4495 USA
Department/Centre: Division of Physical & Mathematical Sciences > Mathematics
Depositing User: Id for Latest eprints
Date Deposited: 30 Oct 2017 03:41
Last Modified: 30 Oct 2017 03:41
URI: http://eprints.iisc.ac.in/id/eprint/58077

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