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February 2019 On extreme contractions and the norm attainment set of a bounded linear operator
Debmalya Sain
Ann. Funct. Anal. 10(1): 135-143 (February 2019). DOI: 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.

Citation

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Debmalya Sain. "On extreme contractions and the norm attainment set of a bounded linear operator." Ann. Funct. Anal. 10 (1) 135 - 143, February 2019. https://doi.org/10.1215/20088752-2018-0014

Information

Received: 14 May 2018; Accepted: 15 June 2018; Published: February 2019
First available in Project Euclid: 16 January 2019

zbMATH: 07045491
MathSciNet: MR3899962
Digital Object Identifier: 10.1215/20088752-2018-0014

Subjects:
Primary: 46B20
Secondary: 46C15

Rights: Copyright © 2019 Tusi Mathematical Research Group

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Vol.10 • No. 1 • February 2019
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