Structure of elementary operators defining $m$-left invertible, $m$-selfadjoint and related classes of operators

TL;DR

This paper investigates the algebraic structure of certain classes of Banach space operators, such as m-invertible, m-isometric, and m-selfadjoint operators, revealing new deep structural properties.

Contribution

It introduces new algebraic insights into the structure of m-invertible, m-isometric, and m-selfadjoint operators using elementary algebraic properties.

Findings

Deep structural properties of m-invertible operators uncovered

Enhanced understanding of m-isometric and m-selfadjoint operators

Adds value to existing operator theory results

Abstract

We use elementary algebraic properties of left, right multiplication operators to prove some deep structural properties of left $m$-invertible, $m$-isometric, $m$-selfadjoint and other related classes of Banach space operators, often adding value to extant results.