TY  - BOOK
AU  - Junge,Marius
AU  - Palazuelos,Carlos
AU  - Parcet,Javier
AU  - Perrin,Mathilde
TI  - Hypercontractivity in group Von Neumann algebras
T2  - Memoirs of the American Mathematical Society
SN  - 9781470425654 (alk. paper)
U1  - 510 23
PY  - 2017///
CY  - Providence : 
PB  - American Mathematical Society
KW  - Von Neumann algebras
KW  - Group algebras
N1  - Includes bibliographical references; 1. The combinatorial method --
2. Optimal time estimates --
3. Poisson-like lengths --
Appendix A. Logarithmic Sobolev inequalities --
Appendix B. The word length in $\mathbb {Z}_n$ --
Appendix C. Numerical analysis --
Appendix D. Technical inequalities --
Bibliography
N2  - Provides a combinatorial/numerical method to establish new hypercontractivity estimates in group von Neumann algebras. The authors 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
ER  -