Property RD and Hypercontractivity for Orthogonal Free Quantum Groups-Reference-Cited by-同舟云学术

Property RD and Hypercontractivity for Orthogonal Free Quantum Groups

Published:2020-05-19 Issue:2 Volume:2021 Page:1573-1601
ISSN:1073-7928
Container-title:International Mathematics Research Notices
language:en
Short-container-title:

Author:

Brannan Michael¹,Vergnioux Roland²,Youn Sang-Gyun³

Affiliation:

1. Department of Mathematics, Mailstop 3368, Texas A & M University, College Station, TX 77843-3368, USA

2. Normandie Univ, UNICAEN,CNRS, LMNO, 14000 Caen, France

3. Department of Mathematics Education, Seoul National University, Gwanak-ro 1, Gwanak-gu, Seoul, 08826, Republic of Korea

Abstract

Abstract We prove that the twisted property RD introduced in [ 2] fails to hold for all non-Kac type, non-amenable orthogonal free quantum groups. In the Kac case we revisit property RD, proving an analogue of the $L_p-L_2$ non-commutative Khintchine inequality for free groups from [ 29]. As an application, we give new and improved hypercontractivity and ultracontractivity estimates for the generalized heat semigroups on free orthogonal quantum groups, both in the Kac and non-Kac cases.

Funder

Natural Science Foundation

Agence Nationale de la Recherche

National Research Foundation

Publisher

Oxford University Press (OUP)

Subject

General Mathematics

Link

http://academic.oup.com/imrn/article-pdf/2021/2/1573/35885646/rnaa118.pdf

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