Standard homogeneous C*-algebras as compact quantum metric spaces

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F20%3A00540451" target="_blank" >RIV/67985840:_____/20:00540451 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.4064/bc120-7" target="_blank" >http://dx.doi.org/10.4064/bc120-7</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.4064/bc120-7" target="_blank" >10.4064/bc120-7</a>

Result language
angličtina
Original language name
Standard homogeneous C*-algebras as compact quantum metric spaces
Original language description
Given a compact metric space X and a unital C*-algebra A, we introduce a family of seminorms on the C*-algebra of continuous functions from X to A, denoted by C(X,A), induced by classical Lipschitz seminorms that produce compact quantum metrics in the sense of Rieffel if and only if A is finite-dimensional. As a consequence, we are able to isometrically embed X into the state space of C(X,A). Furthermore, we are able to extend convergence of compact metric spaces in the Gromov–Hausdorff distance to convergence of spaces of matrices over continuous functions on the associated compact metric spaces in Latrémolière’s Gromov–Hausdorff propinquity.
Czech name
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Czech description
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Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2020
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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