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Hypercontractivity of heat semigroups on free quantum groups

Authors :
François Lemeux
Haonan Zhang
Guixiang Hong
Uwe Franz
Michaël Ulrich
Laboratoire de Mathématiques de Besançon (UMR 6623) (LMB)
Université de Bourgogne (UB)-Université de Franche-Comté (UFC)
Université Bourgogne Franche-Comté [COMUE] (UBFC)-Université Bourgogne Franche-Comté [COMUE] (UBFC)-Centre National de la Recherche Scientifique (CNRS)
School of Mathematics and Statistics [Wuhan University]
Wuhan University [China]
Source :
Journal of Operator Theory, Journal of Operator Theory, Theta Foundation, 2017, 77 (1), pp.61-76. ⟨10.7900/jot.2015nov13.2126⟩
Publication Year :
2017
Publisher :
HAL CCSD, 2017.

Abstract

In this paper we study two semigroups of completely positive unital self-adjoint maps on the von Neumann algebras of the free orthogonal quantum group $O_N^+$ and the free permutation quantum group $S_N^+$. We show that these semigroups satisfy ultracontractivity and hypercontractivity estimates. We also give results regarding spectral gap and logarithmic Sobolev inequalities.<br />19 pages

Details

Language :
English
ISSN :
03794024 and 18417744
Database :
OpenAIRE
Journal :
Journal of Operator Theory, Journal of Operator Theory, Theta Foundation, 2017, 77 (1), pp.61-76. ⟨10.7900/jot.2015nov13.2126⟩
Accession number :
edsair.doi.dedup.....f95deda1f33ee7cb23265bb26938f9f7
Full Text :
https://doi.org/10.7900/jot.2015nov13.2126⟩