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arXiv · 1802.10439

On the norm attainment set of a bounded linear operator and semi-inner-products in normed spaces

Debmalya Sain
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Abstract

We obtain a complete characterization of the norm attainment set of a bounded linear functional on a normed space, in terms of a semi-inner-product defined on the space. Motivated by this result, we further apply the concept of semi-inner-products to obtain a complete characterization of the norm attainment set of a bounded linear operator between any two real normed spaces. In particular, this answers an open question raised recently in [Sain, D., \textit{On the norm attainment set of a bounded linear operator}, J. Math. Anal. Appl., \textbf{457} (2018), 67-76.]. Our results illustrate the applicability of semi-inner-products towards a better understanding of the geometry of normed spaces.

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Debmalya Sain. 2018-02-28. On the norm attainment set of a bounded linear operator and semi-inner-products in normed spaces. https://arxiv.org/abs/1802.10439

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