Unbounded generalizations of the Fuglede-Putnam theorem and applications to the commutativity of self-adjoint operators

TL;DR

This paper explores new unbounded generalizations of the Fuglede-Putnam theorem, providing conditions for the commutativity of bounded self-adjoint and unbounded symmetric operators, with both proofs and counterexamples.

Contribution

It introduces novel unbounded generalizations of the Fuglede-Putnam theorem and establishes conditions for operator commutativity, expanding theoretical understanding.

Findings

Several unbounded generalizations of the Fuglede-Putnam theorem are proved and disproved.

Conditions for commutativity between bounded self-adjoint and unbounded symmetric operators are established.

The paper provides both theoretical results and illustrative examples.

Abstract

In this article, we prove and disprove several generalizations of unbounded versions of the Fuglede-Putnam theorem. As applications, we give conditions guaranteeing the commutativity of a bounded self-adjoint operator with an unbounded closed symmetric operator.