Completely positive maps on Coxeter groups and the ultracontractivity of the q-Ornstein-Uhlenbeck semigroup
Bożejko, Marek
Banach Center Publications, Tome 43 (1998), p. 87-93 / Harvested from The Polish Digital Mathematics Library
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Publié le : 1998-01-01
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     author = {Bo\.zejko, Marek},
     title = {Completely positive maps on Coxeter groups and the ultracontractivity of the q-Ornstein-Uhlenbeck semigroup},
     journal = {Banach Center Publications},
     volume = {43},
     year = {1998},
     pages = {87-93},
     zbl = {0948.47040},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-bcpv43i1p87bwm}
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Bożejko, Marek. Completely positive maps on Coxeter groups and the ultracontractivity of the q-Ornstein-Uhlenbeck semigroup. Banach Center Publications, Tome 43 (1998) pp. 87-93. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-bcpv43i1p87bwm/

[000] [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.

[001] [Bia] Ph. Biane, Free Hypercontractivity, Prepublication N 350, Paris VI, (1996), 1-19.

[002] [B1] M. Bożejko, Positive definite kernels, length functions on groups and a noncommutative von Neumann inequality, Studia Math. 95 (1989), 107-118. | Zbl 0714.43007

[003] [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.

[004] [B3] M. Bożejko, Ultracontractivity and strong Sobolev inequality for q-Ornstein-Uhlenbeck semigroup (to appear). | Zbl 1071.47510

[005] [BSp1] M. Bożejko and R. Speicher, An Example of a Generalized Brownian Motion, Comm. Math. Phys. 137 (1991), 519-531. | Zbl 0722.60033

[006] [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.

[007] [BSp3] M. Bożejko and R. Speicher, Interpolation between bosonic and fermionic relations given by generalized Brownian motions, Math. Zeit. 222 (1996), 135-160.

[008] [BSp4] M. Bożejko and R. Speicher, Completely positive maps on Coxeter Groups, deformed commutation relations, and operator spaces, Math. Annalen 300 (1994), 97-120. | Zbl 0819.20043

[009] [BKS] M. Bożejko, B. Kümmerer and R. Speicher, q-Gaussian Processes: Non-commutative and Classical Aspects, Comm. Math. Phys. 185 (1997),129-154. | Zbl 0873.60087

[010] [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.

[011] [Buch] A. Buchholz, Norm of convolution by operator-valued functions on free groups, Proc. Amer. Math. Soc., (1997).

[012] [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. | Zbl 0796.46054

[013] [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.

[014] [DL] E. B. Davies and J. M. Lindsay, Non-commutative symmetric Markov semigroups, Math. Zeit. 210 (1992), 379-411. | Zbl 0761.46051

[015] [G] L. Gross, Hypercontractivity and logarithmic Sobolev inequalities for the Clifford-Dirichlet form, Duke Math. J. 42 (1975), 383-396. | Zbl 0359.46038

[016] [H] U. Haagerup, An example of a non nuclear C*- algebra which has the metric approximation property, Invent. Math. 50 (1979), 279-293. | Zbl 0408.46046

[017] [HP] U. Haagerup and G. Pisier, Bounded linear operators between C*-algebras, Duke Math. J. 71 (1993), 889-925. | Zbl 0803.46064

[018] [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. | Zbl 0864.46047

[019] [N] E. Nelson, The free Markoff field, J. Func. Anal. 12 (1973), 211-227. | Zbl 0273.60079

[020] [P] G. Pisier, The Operator Hilbert Space OH, Complex Interpolation and Tensor Norms, Mem. Amer. Math.Soc. 1996. | Zbl 0932.46046

[021] [Spe] R. Speicher, A non commutative central limit theorem, Math. Zeit. 209 (1992), 55-66. | Zbl 0724.60023

[022] [VDN] D. V. Voiculescu, K. Dykema and A. Nica, Free random variables, CRM Monograph Series No.1, Amer. Math. Soc., Providence, RI, 1992.

[023] [Z] D. Zagier, Realizability of a model in infinity statistics, Comm. Math. Phys. 147 (1992), 199-210. | Zbl 0789.47042