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Transactions of the American Mathematical Society

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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
MathSciNet review: 3646772
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Abstract: We prove that $\lambda _g\mapsto e^{-t|g|^r}\lambda _g$ 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.


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Additional Information

Tao Mei
Affiliation: Department of Mathematics, Baylor University, One Bear Place #97328, Waco, Texas 76798
MR Author ID: 610890
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

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