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


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


Campbell Hall 443


Dr. Christoph Fischbacher


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.