Various notions of norm-attainability in normed spaces

Benard Okelo

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arXiv · 2004.05496

Various notions of norm-attainability in normed spaces

Benard Okelo

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Abstract

Let $H$ be a reflexive, dense, separable, infinite dimensional complex Hilbert space and let $B(H)$ be the algebra of all bounded linear operators on $H$. In this paper, we carry out characterizations of norm-attainable operators in normed spaces. We give conditions for norm-attainability of linear functionals in Banach spaces, non-power operators on $H$ and elementary operators. Lastly, we characterize a new notion of norm-attainability for power operators in normed spaces.

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Benard Okelo. 2020-04-11. Various notions of norm-attainability in normed spaces. https://arxiv.org/abs/2004.05496

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