On a subclass of norm attaining operators

Ramesh, Golla and Osaka, Hiroyuki (2021) On a subclass of norm attaining operators. Acta Scientiarum Mathematicarum, 87 (12). pp. 247-263. ISSN 0001-6969

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A bounded linear operator T: H1 → H2, where H1, H2 are Hilbert spaces, is said to be norm attaining if there exists a unit vector x ∈ H1 such that kT xk = kT k and absolutely norm attaining (or AN -operator) if T |M: M → H2 is norm attaining for every closed subspace M of H1. We prove a structure theorem for positive operators in β(H):= {T ∈ B(H): T |M: M → M is norm attaining for all M ∈ RT }, where RT is the set of all reducing subspaces of T . We also compare our results with those of absolutely norm attaining operators. Later, we characterize all operators in this new class.

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IITH Creators:
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Item Type: Article
Uncontrolled Keywords: AN-operator; Compact operator; Norm attaining operator; Reducing subspace
Subjects: Mathematics
Divisions: Department of Mathematics
Depositing User: . LibTrainee 2021
Date Deposited: 26 Jul 2021 05:08
Last Modified: 02 Mar 2022 07:16
URI: http://raiith.iith.ac.in/id/eprint/8518
Publisher URL: http://doi.org/10.14232/actasm-020-426-9
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