Completely positive maps on Coxeter groups and the ultracontractivity of the q-Ornstein-Uhlenbeck semigroup

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1. [B] D. Bakry, L'hypercontractivité et son utilisation en théorie des semigroupes, Lectures on Probability Theory, Lecture Notes in Mathematics, vol.1581, Springer, Berlin Heidelberg New York, (1994), 1-114. 
2. [Bia] Ph. Biane, Free Hypercontractivity, Prepublication N 350, Paris VI, (1996), 1-19. 
3. [B1] M. Bożejko, Positive definite kernels, length functions on groups and a noncommutative von Neumann inequality, Studia Math. 95 (1989), 107-118. Zbl0714.43007
4. [B2] M. Bożejko, A q-deformed probability, Nelson's inequality and central limit theorems, Non-linear fields, classical, random, semiclassical (P. Garbaczewski and Z. Popowicz, eds.), World Scientific, Singapore, (1991), 312-335. 
5. [B3] M. Bożejko, Ultracontractivity and strong Sobolev inequality for q-Ornstein-Uhlenbeck semigroup (to appear). Zbl1071.47510
6. [BSp1] M. Bożejko and R. Speicher, An Example of a Generalized Brownian Motion, Comm. Math. Phys. 137 (1991), 519-531. Zbl0722.60033
7. [BSp2] M. Bożejko and R. Speicher, An Example of a generalized Brownian motion II. In : Quantum Probability and Related Topics VII (ed. L. Accardi), Singapore: World Scientific (1992), 219-236. 
8. [BSp3] M. Bożejko and R. Speicher, Interpolation between bosonic and fermionic relations given by generalized Brownian motions, Math. Zeit. 222 (1996), 135-160. 
9. [BSp4] M. Bożejko and R. Speicher, Completely positive maps on Coxeter Groups, deformed commutation relations, and operator spaces, Math. Annalen 300 (1994), 97-120. Zbl0819.20043
10. [BKS] M. Bożejko, B. Kümmerer and R. Speicher, q-Gaussian Processes: Non-commutative and Classical Aspects, Comm. Math. Phys. 185 (1997),129-154. Zbl0873.60087
11. [BSz] M. Bożejko and R. Szwarc, Algebraic length and Poincare series on reflection groups with applications to representations theory, University of Wrocław, preprint (1996), 1-25. 
12. [Buch] A. Buchholz, Norm of convolution by operator-valued functions on free groups, Proc. Amer. Math. Soc., (1997). 
13. [CL] E. A. Carlen and E. H. Lieb, Optimal hypercontractivity for Fermi fields and related non-commutative integration inequalities, Comm. Math. Phys. 155 (1993), 27-46. Zbl0796.46054
14. [CSV] T. Coulhon, L. Saloff-Coste, and N. Th. Varopoulos, Analysis and Geometry on Groups, Cambgidge Tracts in Mathematics, vol.100, Cambridge University Press, 1992. 
15. [DL] E. B. Davies and J. M. Lindsay, Non-commutative symmetric Markov semigroups, Math. Zeit. 210 (1992), 379-411. Zbl0761.46051
16. [G] L. Gross, Hypercontractivity and logarithmic Sobolev inequalities for the Clifford-Dirichlet form, Duke Math. J. 42 (1975), 383-396. Zbl0359.46038
17. [H] U. Haagerup, An example of a non nuclear C*- algebra which has the metric approximation property, Invent. Math. 50 (1979), 279-293. Zbl0408.46046
18. [HP] U. Haagerup and G. Pisier, Bounded linear operators between C*-algebras, Duke Math. J. 71 (1993), 889-925. Zbl0803.46064
19. [JSW] P. E. T. Joergensen, L. M. Schmitt and R. F. Werner, Positive representations of general commutation relations allowing Wick ordering, J. Func. Anal., 134 (1995),3-99. Zbl0864.46047
20. [N] E. Nelson, The free Markoff field, J. Func. Anal. 12 (1973), 211-227. Zbl0273.60079
21. [P] G. Pisier, The Operator Hilbert Space OH, Complex Interpolation and Tensor Norms, Mem. Amer. Math.Soc. 1996. Zbl0932.46046
22. [Spe] R. Speicher, A non commutative central limit theorem, Math. Zeit. 209 (1992), 55-66. Zbl0724.60023
23. [VDN] D. V. Voiculescu, K. Dykema and A. Nica, Free random variables, CRM Monograph Series No.1, Amer. Math. Soc., Providence, RI, 1992. 
24. [Z] D. Zagier, Realizability of a model in infinity statistics, Comm. Math. Phys. 147 (1992), 199-210. Zbl0789.47042