A Criterion for the Normality of Unbounded Operators and Applications to Self-adjointness

TL;DR

This paper introduces a new criterion called 'double maximality' for determining the normality of unbounded operators and applies it to establish conditions for the self-adjointness and normality of operator sums.

Contribution

It presents a novel 'double maximality' criterion for unbounded operators and applies it to derive new results on the self-adjointness and normality of sums of operators.

Findings

Sum of two symmetric operators can be essentially self-adjoint under certain conditions.

Sum of two unbounded normal operators can be essentially normal.

New criterion simplifies analysis of unbounded operator properties.

Abstract

In this paper we give and prove a criterion for the normality of unbounded closed operators, which is a sort of a maximality result which will be called "double maximality". As applications, we show, under some assumptions, that the sum of two symmetric operators is essentially self-adjoint; and that the sum of two unbounded normal operators is essentially normal. Some other important results are also established.