Metrics on trace spaces

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F23%3A00572037" target="_blank" >RIV/67985840:_____/23:00572037 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1016/j.jfa.2023.109977" target="_blank" >https://doi.org/10.1016/j.jfa.2023.109977</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.jfa.2023.109977" target="_blank" >10.1016/j.jfa.2023.109977</a>

Result language
angličtina
Original language name
Metrics on trace spaces
Original language description
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.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/GJ20-17488Y" target="_blank" >GJ20-17488Y: Applications of C*-algebra classification: dynamics, geometry, and their quantum analogues</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2023
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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