Asymmetric Fuglede Putnam's Theorem for operators reduced by their eigenspaces

TL;DR

This paper develops a general spectral theory framework to extend the Fuglede-Putnam theorem to a broader class of operators, especially those reduced by their eigenspaces.

Contribution

It introduces a new theoretical framework using spectral theory to establish the Fuglede-Putnam theorem for more operator classes.

Findings

Framework applicable to various operator classes

Extension of Fuglede-Putnam theorem proved

Spectral theory approach simplifies proofs

Abstract

Fuglede-Putnam Theorem have been proved for a considerably large number of class of operators. In this paper by using the spectral theory, we obtain a theoretical and general framework from which Fuglede-Putnam theorem may be promptly established for many classes of operators.