Tensorial permanence of K‐stability for diagonal AH‐algebras
Abstract
Abstract We study ‐stability for tensor products of diagonal AH‐algebras with arbitrary C*‐algebras. Our main result provides a characterization of ‐stability: For a diagonal AH‐algebra , is ‐stable for every C*‐algebra if and only if the sizes of the matrix blocks in the inductive system grow without bound. As applications, we show that non–‐stable Villadsen algebras of the first kind are ‐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 ‐stable.
Fields of Study & Subjects
Advanced Operator Algebra Research
Functional Equations Stability Results
Advanced Algebra and Logic
Publication details
- Journal / source
- Bulletin of the London Mathematical Society
- Volume
- 58
- Issue
- 5
- Publication date
- 1 May 2026
- Language
- EN