Unbounded generalizations of the Fuglede-Putnam theorem

TL;DR

This paper explores various extensions of the Fuglede-Putnam theorem in the context of unbounded operators, providing both proofs and counterexamples to certain generalizations.

Contribution

It introduces new unbounded generalizations of the Fuglede-Putnam theorem and clarifies which extensions are valid or invalid.

Findings

Some generalizations hold under specific conditions

Counterexamples disprove certain proposed extensions

The paper advances understanding of operator theory in unbounded cases

Abstract

In this paper, we prove and disprove several generalizations of unbounded versions of the Fuglede-Putnam theorem.