Exponentials of Bounded Normal Operators

TL;DR

This paper investigates equations involving exponentials of bounded normal operators, providing conditions for their commutativity without relying on the traditional $2 extpi i$-congruence-free assumption, extending previous research.

Contribution

It introduces new conditions that ensure commutativity of bounded normal operators based on their exponential equations, without the need for the $2 extpi i$-congruence-free hypothesis.

Findings

Conditions for commutativity of normal operators derived

Extension of previous results without $2 extpi i$-congruence-free assumption

Advances understanding of exponential operator equations

Abstract

The present paper is mainly concerned with equations involving exponentials of bounded normal operators. Conditions implying commutativity of those normal operators are given. This is carried out without the known $2\pi i$-congruence-free hypothesis. It is also a continuation of a recent work by the corresponding author.