Exponentials of Normal Operators and Commutativity of Operators: A New Approach

TL;DR

This paper investigates conditions under which the commutativity of exponentials of bounded normal operators on a complex Hilbert space implies the commutativity of the operators themselves, introducing a novel approach.

Contribution

It provides a new method to determine when operator exponential commutativity implies operator commutativity for bounded normal operators.

Findings

Established conditions linking exponential and operator commutativity.

Utilized similarities results and Fuglede theorem in proofs.

Extended understanding of operator exponential behavior.

Abstract

We present a new approach to the question of when the commutativity of operator exponentials implies that of the operators. This is proved in the setting of bounded normal operators on a complex Hilbert space. The proofs are based on some similarities results by Berberian and Embry as well as the celebrated Fuglede theorem.