Metrics on trace spaces

0572037 - MÚ 2024 RIV NL eng J - Journal Article
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
R&D Projects: GA ČR(CZ) GJ20-17488Y
Institutional support: RVO:67985840
Keywords : optimal transport * unitary orbits * Z-stable * C⁎-algebras
OECD category: Pure mathematics
Impact factor: 1.7, year: 2022
Method of publishing: Limited access
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.
Permanent Link: https://hdl.handle.net/11104/0342875