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ON EXTREME CONTRACTIONS AND THE NORM ATTAINMENT SET OF A BOUNDED LINEAR OPERATOR

Sain, Debmalya (2019) ON EXTREME CONTRACTIONS AND THE NORM ATTAINMENT SET OF A BOUNDED LINEAR OPERATOR. In: ANNALS OF FUNCTIONAL ANALYSIS, 10 (1). pp. 135-143.

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Official URL: https://doi.org/10.1215/20088752-2018-0014

Abstract

In this paper we completely characterize the norm attainment set of a bounded linear operator between Hilbert spaces. In fact, we obtain two different characterizations of the norm attainment set of a bounded linear operator between Hilbert spaces. We further study the extreme contractions on various types of finite-dimensional Banach spaces, namely Euclidean spaces, and strictly convex spaces. In particular, we give an elementary alternative proof of the well-known characterization of extreme contractions on a Euclidean space, which works equally well for both the real and the complex case. As an application of our exploration, we prove that it is possible to characterize real Hilbert spaces among real Banach spaces, in terms of extreme contractions on their 2-dimensional subspaces.

Item Type: Journal Article
Additional Information: Copyright of this article belongs to
Keywords: extreme contractions; operator-norm attainment; isometry; characterization of Hilbert spaces
Department/Centre: Division of Physical & Mathematical Sciences > Mathematics
Depositing User: Francis Jayakanth
Date Deposited: 10 Feb 2019 09:52
Last Modified: 10 Feb 2019 09:52
URI: http://eprints.iisc.ac.in/id/eprint/61633

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