### Perturbation of minimum attaining operators

#### 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.

#### Article information

Source
Adv. Oper. Theory Volume 3, Number 3 (2018), 473-490.

Dates
Accepted: 20 December 2017
First available in Project Euclid: 7 February 2018

https://projecteuclid.org/euclid.aot/1518016380

Digital Object Identifier
doi:10.15352/aot.1708-1215

#### Citation

Ganesh, Jadav; Ramesh, Golla; Sukumar, Daniel. Perturbation of minimum attaining operators. Adv. Oper. Theory 3 (2018), no. 3, 473--490. doi:10.15352/aot.1708-1215. https://projecteuclid.org/euclid.aot/1518016380

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