Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Complete boundedness of heat semigroups on the von Neumann algebra of hyperbolic groups


Authors: Tao Mei and Mikael de la Salle
Journal: Trans. Amer. Math. Soc. 369 (2017), 5601-5622
MSC (2010): Primary 20E05, 20F67, 43A22
DOI: https://doi.org/10.1090/tran/6825
Published electronically: January 9, 2017
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We prove that $ \lambda _g\mapsto e^{-t\vert g\vert^r}\lambda _g$ defines a multiplier on the von Neuman algebra of hyperbolic groups with a complete bound $ \simeq r$, for any $ 0<t<\infty , 1<r<\infty $. In the proof we observe that a construction of Ozawa allows us to characterize the radial multipliers that are bounded on every hyperbolic graph, partially generalizing results of Haagerup-Steenstrup-Szwarc and Wysoczański. Our argument is also based on the work of Peller.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (2010): 20E05, 20F67, 43A22

Retrieve articles in all journals with MSC (2010): 20E05, 20F67, 43A22


Additional Information

Tao Mei
Affiliation: Department of Mathematics, Baylor University, One Bear Place #97328, Waco, Texas 76798
Email: tao_mei@Baylor.edu

Mikael de la Salle
Affiliation: CNRS-ENS de Lyon, UMPA UMR 5669, F-69364 Lyon cedex 7, France
Email: mikael.de.la.salle@ens-lyon.fr

DOI: https://doi.org/10.1090/tran/6825
Received by editor(s): March 20, 2015
Received by editor(s) in revised form: September 8, 2015
Published electronically: January 9, 2017
Additional Notes: The research of the first author was partially supported by NSF grant DMS-1266042.
The research of the second author was partially supported by the ANR projects NEUMANN and OSQPI
Article copyright: © Copyright 2017 American Mathematical Society

American Mathematical Society