Normals, subnormals and an open question

TL;DR

This paper provides a comparative survey of bounded and unbounded subnormal operators, emphasizing their complex structures and relation to normal operators, serving as a practical guide to this intricate area of operator theory.

Contribution

It offers a practical overview of unbounded subnormal operators, highlighting their structure and relationship with normal operators, filling a gap in the existing literature.

Findings

Unbounded subnormal operators have the richest structure among related classes.

Normal operators serve as a reference point for understanding subnormality.

The paper presents a comparative survey of bounded and unbounded cases.

Abstract

An acute look at \underbar{basic} facts concerning \underbar{unbounded} subnormal operators is taken here. These operators have the richest structure and are the most exciting among the whole family of beneficiaries of the normal ones. Therefore, the latter must necessarily be taken into account as the reference point for any exposition of subnormality. So as to make the presentation more appealing a kind of comparative survey of the bounded and unbounded case has been set forth. \noindent This piece of writing serves rather as a practical guide to this largely impenetrable territory than an exhausting report.