Adjoints and Formal Adjoints of Matrices of Unbounded Operators

TL;DR

This paper explores the relationship between adjoints and formal adjoints of unbounded operators with matrix structures, focusing on how row and column operators influence the properties of the entire matrix operator.

Contribution

It provides a detailed analysis of the interplay between adjoints and formal adjoints in unbounded matrix operators, highlighting the significance of row and column operators.

Findings

Row and column operators determine key properties of matrix operators.

The relationship between adjoints and formal adjoints is clarified for unbounded operators.

Insights into the structure of unbounded matrix operators are provided.

Abstract

In this paper we {\em discuss} diverse aspects of mutual relationship between adjoints and formal adjoints of unbounded operators bearing a matrix structure. We emphasize on the behaviour of row and column operators as they turn out to be the germs of an arbitrary matrix operator, providing most of the information about the latter {as it is the troublemaker}.