This is an announcement for the paper “On the denseness of minimum attaining operators” by S. H. Kulkarnihttps://arxiv.org/find/math/1/au:+Kulkarni_S/0/1/0/all/0/1, G. Rameshhttps://arxiv.org/find/math/1/au:+Ramesh_G/0/1/0/all/0/1.

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 $|S|<\epsilson$ such that $T+S$ is minimum attaining. Further, if $T$ is bounded below, then $S$ can be chosen to be rank one.

The paper may be downloaded from the archive by web browser from URL https://arxiv.org/abs/1609.06869