On a subclass of norm attaining operators

Ramesh Golla and Osaka Hiroyuki: On a subclass of norm attaining operators. In: Acta scientiarum mathematicarum, (87) 1-2. pp. 247-263. (2021)

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Abstract

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 = kTk 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.

Item Type:	Article
Heading title:	Analysis
Journal or Publication Title:	Acta scientiarum mathematicarum
Date:	2021
Volume:	87
Number:	1-2
ISSN:	2064-8316
Page Range:	pp. 247-263
Language:	English
Related URLs:	http://acta.bibl.u-szeged.hu/73791/
DOI:	10.14232/actasm-020-426-9
Uncontrolled Keywords:	Matematika
Additional Information:	Bibliogr.: p. 262-263. ; összefoglalás angol nyelven
Date Deposited:	2021. Nov. 16. 09:07
Last Modified:	2021. Nov. 16. 09:07
URI:	http://acta.bibl.u-szeged.hu/id/eprint/73928

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