Complete boundedness of the Heat Semigroups on the von Neumann Algebra of hyperbolic groups

Abstract

We prove that $({\lambda }_g\mapsto e^{-t|g{|}^r}{\lambda }_g{)}_{t>0}$ defines a completely bounded semigroup of multipliers on the von Neuman algebra of hyperbolic groups for all real number $r$. One ingredient in the proof is the observation that a construction of Ozawa allows to characterize the radial multipliers that are bounded on every hyperbolic graph, partially generalizing results of Haagerup--Steenstrup--Szwarc and Wysoczański. Another ingredient is an upper estimate of trace class norms for Hankel matrices, which is based on Peller's characterization of such norms.

v2: 28 pages, with new examples, new results, motivations and hopefully a better presentation

Cited by in corpus (2)

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