Polynomial approximation of quantum Lipschitz functions

Konrad Aguilar; Jens Kaad; David Kyed

doi:10.25537/dm.2022v27.765-787

Polynomial approximation of quantum Lipschitz functions

Konrad Aguilar^*, Jens Kaad, David Kyed

^*Corresponding author for this work

Department of Mathematics and Computer Science

Research output: Contribution to journal › Journal article › Research › peer-review

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Abstract

We prove an approximation result for Lipschitz functions on the quantum sphere S²_q, from which we deduce that the two natural quantum metric structures on S²_q have quantum Gromov-Hausdorff distance zero.

Original language	English
Journal	Documenta Mathematica
Volume	27
Pages (from-to)	765-787
ISSN	1431-0635
DOIs	https://doi.org/10.25537/dm.2022v27.765-787
Publication status	Published - 2022

Keywords

Berezin transform
Podleś sphere
Quantum metric spaces
fuzzy spheres
quantum GromovHausdorﬀ distance
spectral triples

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10.25537/dm.2022v27.765-787Licence: CC BY

Open Access VersionFinal published version, 281 KBLicence: CC BY

https://arxiv.org/pdf/2104.04317

Cite this

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title = "Polynomial approximation of quantum Lipschitz functions",

abstract = "We prove an approximation result for Lipschitz functions on the quantum sphere S2q, from which we deduce that the two natural quantum metric structures on S2q have quantum Gromov-Hausdorff distance zero.",

keywords = "Berezin transform, Podle{\'s} sphere, Quantum metric spaces, fuzzy spheres, quantum GromovHausdorﬀ distance, spectral triples",

author = "Konrad Aguilar and Jens Kaad and David Kyed",

note = "18 pages",

year = "2022",

doi = "10.25537/dm.2022v27.765-787",

language = "English",

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journal = "Documenta Mathematica",

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T1 - Polynomial approximation of quantum Lipschitz functions

AU - Aguilar, Konrad

AU - Kaad, Jens

AU - Kyed, David

N1 - 18 pages

PY - 2022

Y1 - 2022

N2 - We prove an approximation result for Lipschitz functions on the quantum sphere S2q, from which we deduce that the two natural quantum metric structures on S2q have quantum Gromov-Hausdorff distance zero.

AB - We prove an approximation result for Lipschitz functions on the quantum sphere S2q, from which we deduce that the two natural quantum metric structures on S2q have quantum Gromov-Hausdorff distance zero.

KW - Berezin transform

KW - Podleś sphere

KW - Quantum metric spaces

KW - fuzzy spheres

KW - quantum GromovHausdorﬀ distance

KW - spectral triples

U2 - 10.25537/dm.2022v27.765-787

DO - 10.25537/dm.2022v27.765-787

M3 - Journal article

SN - 1431-0635

VL - 27

SP - 765

EP - 787

JO - Documenta Mathematica

JF - Documenta Mathematica

ER -

Polynomial approximation of quantum Lipschitz functions

Abstract

Keywords

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