Compressions of selfadjoint and maximal dissipative extensions of non-densely defined symmetric operators

TL;DR

This paper investigates the properties and compressions of selfadjoint and maximal dissipative extensions of non-densely defined symmetric operators in infinite-dimensional Hilbert spaces, revealing new characteristics of their characteristic functions.

Contribution

It introduces novel properties of characteristic functions for non-densely defined symmetric operators and analyzes their compressions in the case of infinite codimension.

Findings

New properties of characteristic functions established.

Analysis of compressions in the infinite codimension case.

Insights into extensions of non-densely defined symmetric operators.

Abstract

Selfadjoint and maximal dissipative extensions of a non-densely defined symmetric operator $S$ in an infinite-dimensional separable Hilbert space are considered and their compressions on the subspace ${\rm \overline{dom}\,} S$ are studied. The main focus is on the case ${\rm codim\,}{\rm \overline{dom}\,}S=\infty$. New properties of the characteristic functions of non-densely defined symmetric operators are established.