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arXiv · 2607.24699

Diagonal dimension and intermediate sub-C*-algebras

Grigoris Kopsacheilis
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Abstract

We show that finiteness of diagonal dimension, in the sense of Li--Liao--Winter, passes to intermediate sub-C*-algebras. More specifically, we obtain an upper bound for the diagonal dimension of the pair of an intermediate sub-C*-algebra in a C*-diagonal together with the diagonal, which we estimate in terms of the diagonal dimension of the ambient pair and the covering dimension of the diagonal's spectrum. This generalizes a theorem of Archbold and Kumjian stating that intermediate sub-C*-algebras of AF-diagonals are AF C*-algebras.

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Grigoris Kopsacheilis. 2026-07-27. Diagonal dimension and intermediate sub-C*-algebras. https://arxiv.org/abs/2607.24699

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