The nuclear dimension of extensions of commutative C*-algebras by the compact operators

TL;DR

This paper proves that the nuclear dimension of certain C*-algebra extensions equals the topological dimension of the underlying space, generalizing previous results for the Toeplitz algebra.

Contribution

It establishes a general result linking nuclear dimension of extensions of commutative C*-algebras by compact operators to the space's dimension.

Findings

Nuclear dimension of extensions equals the dimension of the base space.

Generalizes the Toeplitz algebra case to broader classes of extensions.

Provides a dimension-theoretic characterization of nuclear dimension.

Abstract

Generalizing the case of the Toeplitz algebra by Brake and Winter, we prove that the nuclear dimension of a C*-algebra extension of C(X) by the compact operators is equal to the dimension of X.