{"product_id":"9781470425654","title":"Hypercontractivity in Group von Neumann Algebras","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 $L2 \\to Lq$ inequalities with respect to the Markov process given by the word length and with $q$ an even integer. Interpolation and differentiation also yield general $Lp \\to Lq$ hypercontrativity for $1 The authors also develop another combinatorial method which does not rely on computational estimates and provides (non-optimal) $Lp \\to Lq$ 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).","brand":"Marius Junge","offers":[{"title":"Default Title","offer_id":46776535712062,"sku":"9781470425654","price":0.0,"currency_code":"ZAR","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4357\/7662\/products\/9781470425654_d106f783-4e5b-4be0-b1df-8e3ba0d1a257.jpg?v=1707476979","url":"https:\/\/exclusivebooks.co.za\/products\/9781470425654","provider":"Exclusive Books Online","version":"1.0","type":"link"}