Metrics on trace spaces

0572037 - MÚ 2024 RIV NL eng J - Článek v odborném periodiku
Jacelon, Bhishan
Metrics on trace spaces.
Journal of Functional Analysis. Roč. 285, č. 4 (2023), č. článku 109977. ISSN 0022-1236. E-ISSN 1096-0783
Grant CEP: GA ČR(CZ) GJ20-17488Y
Institucionální podpora: RVO:67985840
Klíčová slova: optimal transport * unitary orbits * Z-stable * C⁎-algebras
Obor OECD: Pure mathematics
Impakt faktor: 1.7, rok: 2022
Způsob publikování: Omezený přístup
https://doi.org/10.1016/j.jfa.2023.109977

This article continues the investigation of the tracial geometry of classifiable C*-algebras that have real rank zero and stable rank one. Using the language of optimal transport, we describe several situations in which the distance between unitary orbits of ⁎-homomorphisms into such algebras can be computed in terms of tracial data. The domains we consider are certain (noncommutative) CW complexes, and the measurement is relative to a family of self-adjoint elements that are in a suitable sense tracially Lipschitz. As another application of the utility of this Lipschitz structure, we show how such elements can be repurposed to witness statistical features of endomorphisms in the classifiable category, in particular the tracial version of the (almost-sure) central limit theorem.
Trvalý link: https://hdl.handle.net/11104/0342875