%0 Journal Article
%T Perturbation of minimum attaining operators
%J Advances in Operator Theory
%I Tusi Mathematical Research Group (TMRG)
%Z 2538-225X
%A Ganesh, Jadav
%A Ramesh, Golla
%A Sukumar, Daniel
%D 2018
%\ 07/01/2018
%V 3
%N 3
%P 473-490
%! Perturbation of minimum attaining operators
%K minimum modulus
%K spectrum
%K essential spectrum
%K porous set
%R 10.15352/aot.1708-1215
%X 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.
%U http://www.aot-math.org/article_54270_bc17d5d42fb655dade72954a6c56fd0a.pdf