The essential centre of the mod a diagonalization ideal commutant of an n-tuple of commuting hermitian operators

TL;DR

This paper characterizes the essential center of the algebra of operators commuting with a commuting n-tuple of hermitian operators with perfect spectrum, linking it to the C*-algebra and addressing questions related to normal operators and K-theory.

Contribution

It establishes that the essential center arises from the C*-algebra of the n-tuple, providing new insights into the structure of commutants mod diagonalization ideals.

Findings

The essential center is derived from the C*-algebra of the n-tuple.

Answers a question for normal operators and the Hilbert-Schmidt class.

Connects the algebraic structure to K-theory for almost normal operators.

Abstract

We show that for a commuting n-tuple of hermitian operators, with perfect spectrum, the essential centre of the algebra of operators commuting with the n-tuple mod a diagonalization ideal arises from the C*-algebra of the n-tuple. This answers a question for normal operators and the Hilbert-Schmidt class connected to K-theory for almost normal operators.