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Metrics on trace spaces
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SYSNO ASEP 0572037 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title Metrics on trace spaces Author(s) Jacelon, Bhishan (MU-W) SAI Article number 109977 Source Title Journal of Functional Analysis. - : Elsevier - ISSN 0022-1236
Roč. 285, č. 4 (2023)Number of pages 32 s. Language eng - English Country NL - Netherlands Keywords optimal transport ; unitary orbits ; Z-stable ; C⁎-algebras Subject RIV BA - General Mathematics OECD category Pure mathematics R&D Projects GJ20-17488Y GA ČR - Czech Science Foundation (CSF) Method of publishing Limited access Institutional support MU-W - RVO:67985840 UT WOS 000999073700001 EID SCOPUS 85154597907 DOI 10.1016/j.jfa.2023.109977 Annotation 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. Workplace Mathematical Institute Contact Jarmila Štruncová, struncova@math.cas.cz, library@math.cas.cz, Tel.: 222 090 757 Year of Publishing 2024 Electronic address https://doi.org/10.1016/j.jfa.2023.109977
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