On the denseness of minimum attaining operators

S. H. Kulkarni; G. Ramesh

On the denseness of minimum attaining operators

Functional Analysis 2016-09-23 v1

Authors: S. H. Kulkarni , G. Ramesh

Abstract

Let $H_1,H_2$ be complex Hilbert spaces and $T$ be a densely defined closed linear operator (not necessarily bounded). It is proved that for each $\epsilon>0$ , there exists a bounded operator $S$ with $\|S\|\leq \epsilon$ such that $T+S$ is minimum attaining. Further, if $T$ is bounded below, then $S$ can be chosen to be rank one.

Keywords

operator theory on hilbert spaces numerical range operator theory

Cite

@article{arxiv.1609.06869,
  title  = {On the denseness of minimum attaining operators},
  author = {S. H. Kulkarni and G. Ramesh},
  journal= {arXiv preprint arXiv:1609.06869},
  year   = {2016}
}

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