A similarity invariant of a class of n-normal operators in terms of K-theory

TL;DR

This paper extends the Jordan canonical form concept to a specific class of n-normal operators on Hilbert spaces using von Neumann's reduction theory and introduces a K-theory-based similarity invariant.

Contribution

It provides a new analogue of the Jordan form for n-normal operators and establishes a K-theory-based similarity invariant for this class.

Findings

Analogous Jordan form for n-normal operators established

Complete similarity invariant characterized by K-theory

Advances understanding of operator classification in functional analysis

Abstract

In this paper, we prove an analogue of the Jordan canonical form theorem for a class of $n$-normal operators on complex separable Hilbert spaces in terms of von Neumann's reduction theory. This is a continuation of our study of bounded linear operators, the commutants of which contain bounded maximal abelian set of idempotents. Furthermore, we give a complete similarity invariant for this class of operators by $K$-theory for Banach algebras.