Half-centered Operators

TL;DR

This paper investigates half-centered operators on Hilbert spaces, providing conditions under which they are centered and establishing a structure theorem for a specific subclass, advancing understanding of their algebraic properties.

Contribution

It introduces criteria for when half-centered operators are centered and proves a new structure theorem for a particular class of these operators.

Findings

Conditions for half-centered operators to be centered

A structure theorem for a subclass of half-centered operators

Enhanced understanding of the algebraic structure of these operators

Abstract

An operator $T$ on a Hilbert space is called half-centered if the sequence $T^{*}T,(T^{*})^{2}T^{2},...$ consists of mutually commuting operators. It is a subclass of the well-studied centered operators. In this paper we give a condition for when a half-centered operator is centered and prove a structure theorem for those half-centered operators that satisfies a criteria of a technical nature.