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Hypercontractivity in Group von Neumann Algebras (Memoirs of the American Mathematical Society)

Algebra

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Product Description In this paper, the authors provide a combinatorial/numerical method to establish new hypercontractivity estimates in group von Neumann algebras. They illustrate their method with free groups, triangular groups and finite cyclic groups, for which they obtain optimal time hypercontractive $L_2 \to L_q$ inequalities with respect to the Markov process given by the word length and with $q$ an even integer. Interpolation and differentiation also yield general $L_p \to L_q$ hypercontrativity for $1 The authors also develop another combinatorial method which does not rely on computational estimates and provides (non-optimal) $L_p \to L_q$ hypercontractive inequalities for a larger class of groups/lengths, including any finitely generated group equipped with a conditionally negative word length, like infinite Coxeter groups. The authors' second method also yields hypercontractivity bounds for groups admitting a finite dimensional proper cocycle. Hypercontractivity fails for conditionally negative lengths in groups satisfying Kazhdan's property (T). About the Author Marius Junge, University of Illinois at Urbana-Champaign, Illinois.Carlos Palazuelos, Instituto de Ciencias Matematicas, Madrid, Spain.Javier Parcet, Instituto de Ciencias Matematicas, Madrid, Spain.Mathilde Perrin, Instituto de Ciencias Matematicas, Madrid, Spain.

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Format: Paperback
ASIN: 1470425653
Category: Books > Subjects > Science, Nature & Maths > Mathematics > Algebra
Domain: Amazon UK
Release Date: 30 October 2017
Listed Since: 28 June 2017

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Hypercontractivity in Group von Neumann Algebras (Memoirs of the American Mathematical Society)

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