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

Mei, Tao; de la Salle, Mikael

doi:10.1090/tran/6825

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.

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