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zbMATH Open
Article . 2024
Data sources: zbMATH Open
https://dx.doi.org/10.48550/ar...
Article . 2022
License: CC BY
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The Fell topology and the modular Gromov-Hausdorff propinquity

Authors: Aguilar, Konrad; Yu, Jiahui;

The Fell topology and the modular Gromov-Hausdorff propinquity

Abstract

We show that any (norm-closed two-sided) ideal of a unital C*-algebra that comes equipped with certain natural quantum metric structure is a metrized quantum vector bundle, when canonically viewed as a module over A A . Next, given a unital AF-algebra A A equipped with a faithful tracial state, we equip each ideal of A A with a metrized quantum vector bundle structure using previous work of the first author and Latrémolière. Moreover, we show that convergence of ideals in the Fell topology implies convergence of the associated metrized quantum vector bundles in the modular Gromov-Hausdorff propinquity of Latrémolière. In a similar vein but requiring a different approach, given a compact metric space ( X , d ) (X,d) , we equip each ideal of C ( X ) C(X) with a metrized quantum vector bundle structure, and show that convergence in the Fell topology implies convergence in the modular Gromov-Hausdorff propinquity.

Related Organizations
Keywords

Fell topology, modular Gromov-Hausdorff propinquity, States of selfadjoint operator algebras, quantum vector bundles, 46L89, 46L30, 58B34, Noncommutative geometry (à la Connes), Other ``noncommutative'' mathematics based on \(C^*\)-algebra theory, quantum metric, Mathematics - Operator Algebras, FOS: Mathematics, Operator Algebras (math.OA)

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
0
Average
Average
Average
Green