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Summer 2018 Perturbation of minimum attaining operators
Jadav Ganesh, Golla Ramesh, Daniel Sukumar
Adv. Oper. Theory 3(3): 473-490 (Summer 2018). DOI: 10.15352/aot.1708-1215

Abstract

We prove that the minimum attaining property of a bounded linear operator on a Hilbert space $H$ whose minimum modulus lies in the discrete spectrum, is stable under small compact perturbations. We also observe that given a bounded operator with strictly positive essential minimum modulus, the set of compact perturbations which fail to produce a minimum attaining operator is smaller than a nowhere dense set. In fact, it is a porous set in the ideal of all compact operators on $H$. Further, we try to extend these stability results to perturbations by all bounded linear operators with small norm and obtain subsequent results.

Citation

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Jadav Ganesh. Golla Ramesh. Daniel Sukumar. "Perturbation of minimum attaining operators." Adv. Oper. Theory 3 (3) 473 - 490, Summer 2018. https://doi.org/10.15352/aot.1708-1215

Information

Received: 10 August 2017; Accepted: 20 December 2017; Published: Summer 2018
First available in Project Euclid: 7 February 2018

zbMATH: 06902447
MathSciNet: MR3795095
Digital Object Identifier: 10.15352/aot.1708-1215

Subjects:
Primary: 47B07
Secondary: 47A10, 47A55, 47B65

Rights: Copyright © 2018 Tusi Mathematical Research Group

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Vol.3 • No. 3 • Summer 2018
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