Generalized Polar Decompositions for Closed Operators in Hilbert Spaces and Some Applications

TL;DR

This paper explores generalized polar decompositions of closed operators in Hilbert spaces and applies these findings to analyze perturbations of various classes of operators, enhancing understanding of their stability and spectral properties.

Contribution

It introduces a framework for generalized polar decompositions of closed operators and demonstrates their applications to perturbation theory in operator analysis.

Findings

Established new forms of polar decompositions for closed operators.

Applied these decompositions to study perturbations of self-adjoint and normal operators.

Provided insights into the stability of spectral properties under perturbations.

Abstract

We study generalized polar decompositions of densely defined, closed linear operators in Hilbert spaces and provide some applications to relatively (form) bounded and relatively (form) compact perturbations of self-adjoint, normal, and m-sectorial operators.