On determining the domain of the adjoint operator

TL;DR

This paper presents a theorem to help determine the domain of the adjoint operator, aiding in assessing properties like selfadjointness, normality, and H-selfadjointness in various operators.

Contribution

It introduces a new theorem that provides criteria for the domain of the adjoint operator, applicable to differential and matrix operators.

Findings

The theorem aids in computing the adjoint's domain.

It offers criteria for selfadjointness and normality.

Examples include differential and infinite matrix operators.

Abstract

A theorem that is of aid in computing the domain of the adjoint operator is provided. It may serve e.g. as a criterion for selfadjointness of a symmetric operator, for normality of a formally normal operator or for $H$--selfadjointness of an $H$--symmetric operator. Differential operators and operators given by an infinite matrix are considered as examples.