More on the Normality of the Unbounded Product of Two Normal Operators

TL;DR

This paper investigates conditions under which the product of two possibly unbounded normal operators remains normal, extending existing results and generalizing previous findings on normal matrix products.

Contribution

It introduces new conditions for the normality of the product of two unbounded normal operators and generalizes prior results on normal matrix products.

Findings

Derived new criteria for normality of operator products

Extended results to unbounded operators

Generalized matrix product normality conditions

Abstract

Let $A$ and $B$ be two -non necessarily bounded- normal operators. We give new conditions making their product normal. We also generalize a result by Deutsch et al on normal products of matrices.