Abstract:We study $K$-stability for tensor products of diagonal AH-algebras with arbitrary C*-algebras. Our main result provides a characterization of $K$-stability: for a diagonal AH-algebra $A = \varinjlim (A_i, \varphi_i)$, $A \otimes B$ is $K$-stable for every C*-algebra $B$ if and only if the sizes of the matrix blocks in the inductive system grow without bound. As applications, we show that non-$\mathcal{Z}$-stable Villadsen algebras of the first kind are $K$-stable when tensored with any C*-algebra. Moreover, any simple, unital, infinite-dimensional diagonal AH-algebra automatically satisfies this growth condition, and therefore its tensor product with arbitrary C*-algebras is always $K$-stable.
| Comments: | Replaced with the accepted manuscript |
| Subjects: | Operator Algebras (math.OA) |
| MSC classes: | 46L85 (Primary) 46L80 (Secondary) |
| Cite as: | arXiv:2512.04780 [math.OA] |
| (or arXiv:2512.04780v2 [math.OA] for this version) | |
| https://doi.org/10.48550/arXiv.2512.04780 arXiv-issued DOI via DataCite |
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| Journal reference: | Bull. Lond. Math. Soc. 58 (2026) |
| Related DOI: | https://doi.org/10.1112/blms.70398
DOI(s) linking to related resources |
From: Apurva Seth [view email]
[v1]
Thu, 4 Dec 2025 13:25:59 UTC (19 KB)
[v2]
Fri, 22 May 2026 16:00:56 UTC (24 KB)
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