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

Debmalya Sain ()
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Debmalya Sain: Indian Institute of Science

Indian Journal of Pure and Applied Mathematics, 2020, vol. 51, issue 1, 179-186

Abstract: 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.

Keywords: Normed space; linear operator; norm attainment; semi-inner-product; 47A05; 46B20 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s13226-020-0393-9

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