Fuglede-Putnam theorem for locally measurable operators

TL;DR

This paper extends the Fuglede-Putnam theorem to the broader setting of locally measurable operators affiliated with von Neumann algebras, expanding its applicability beyond bounded operators.

Contribution

It introduces a generalization of the Fuglede-Putnam theorem to locally measurable operators in von Neumann algebra contexts.

Findings

Fuglede-Putnam theorem successfully extended to locally measurable operators.

The generalization broadens the theorem's applicability in operator algebra theory.

Provides new tools for analysis in von Neumann algebra frameworks.

Abstract

We extend the Fuglede-Putnam theorem from the algebra $B(H)$ of all bounded operators on the Hilbert space $H$ to the algebra of all locally measurable operators affiliated with a von Neumann algebra.