Journal of Operator Theory

Volume 92, Issue 2, Autumn 2024 pp. 331-348.

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

Authors: Ruaridh Gardner(1) and Aaron Tikuisis (2)
Author institution: (1) Department of Mathematics and Statistics University of Ottawa 150 Louis-Pasteur Ottawa, Canada
(2) Department of Mathematics and Statistics University of Ottawa 150 Louis-Pasteur Ottawa, Canada

Summary: 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 $X$.

DOI: http://dx.doi.org/10.7900/jot.2022oct14.2418
Keywords: nuclear $C^*$-algebras, nuclear dimension, Toeplitz algebras, Brown-Douglas-Fillmore theory

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