Commutativity of Unbounded Normal and Self-adjoint Operators and Applications

TL;DR

This paper explores the conditions under which unbounded normal and self-adjoint operators commute, extending previous foundational results and demonstrating their applications in operator theory.

Contribution

It generalizes existing results on operator commutativity, providing new proofs and applications for unbounded normal and self-adjoint operators.

Findings

Established new conditions for operator commutativity.

Extended classical results to broader classes of operators.

Demonstrated applications in mathematical physics and functional analysis.

Abstract

Devinatz, Nussbaum and von Neumann established some important results on the strong commutativity of self-adjoint and normal unbounded operators. In this paper, we prove results in the same spirit.