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

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- by Tao Mei and Mikael de la Salle PDF
- Trans. Amer. Math. Soc.
**369**(2017), 5601-5622 Request permission

## 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.## References

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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 - © Copyright 2017 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**369**(2017), 5601-5622 - MSC (2010): Primary 20E05, 20F67, 43A22
- DOI: https://doi.org/10.1090/tran/6825
- MathSciNet review: 3646772