## A Birman-Krein-Vishik-Grubb (BKVG) Theory for Sectorial Operators

### When

November 2, 2018 | 2:30 - 3:30 p.m.

### Speaker

Dr. Christoph Fischbacher

### Abstract

This talk is split in two parts. Firstly, we will review and discuss classical results by Birman, Krein, Vishik, and Grubb on the theory of non-negative selfadjoint extensions of a strictly positive symmetric operator $S$ on a complex Hilbert space. In particular, we will see that any such extension $\widehat{S}$ satisfies $S_K\leq\widehat{S}\leq S_F$, where $S_F$ and $S_K$ are the exceptional Friedrichs and Krein-von Neumann extensions of $S$, respectively. After this, we will discuss what happens if $S$ is perturbed by a skew-symmetric operator of the form $iV$, where $V$ is symmetric such that $A=S+iV$ is sectorial and derive a modified BKVG theory for this case.