L∞-Khintchine-Bonami inequality in free probability
Buchholz, Artur
Banach Center Publications, Tome 43 (1998), p. 105-109 / Harvested from The Polish Digital Mathematics Library
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We prove the norm estimates for operator-valued functions on free groups supported on the words with fixed length (f=∑|w|=law⊗λ(w)). Next, we replace the translations by the free generators with a free family of operators and prove inequalities of the same type.

Publié le : 1998-01-01
EUDML-ID : urn:eudml:doc:208829 
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     author = {Buchholz, Artur},
     title = {$L\_$\infty$$-Khintchine-Bonami inequality in free probability},
     journal = {Banach Center Publications},
     volume = {43},
     year = {1998},
     pages = {105-109},
     zbl = {0948.47007},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-bcpv43i1p105bwm}
}

Buchholz, Artur. $L_∞$-Khintchine-Bonami inequality in free probability. Banach Center Publications, Tome 43 (1998) pp. 105-109. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-bcpv43i1p105bwm/

[000] [Bo1] M. Bożejko, On Λ(p) sets with minimal constant in discrete noncommutative groups, Proc. Amer. Math. Soc. 51(2) (1975), 407-412. | Zbl 0321.43004

[001] [Bo2] M. Bożejko, A q-deformed probability, Nelson's inequality and central limit theorems, Non-linear fields, classical, random, semiclassical, (eds. P. Garbaczewski and Z. Popowicz), World Scientific, Singapore (1991), 312-335.

[002] [BSp] 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

[003] [Bn] A. Bonami, Étude des coefficients de Fourier des fonctions de Lp(G), Ann. Inst. Fourier 20,2 (1970), 335-402. | Zbl 0195.42501

[004] [Bu] A. Buchholz, Norm of convolution by operator-valued functions on free groups, To appear in Proc. Amer. Math. Soc.

[005] [H1] U. Haagerup, Les meilleures constantes de l'inégalité de Khintchine, C. R. Acad. Soc. Paris 286 (1978), A259-A262. | Zbl 0377.46013

[006] [H2] 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

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

[008] [L] M. Leinert, Multiplikatoren diskreter Gruppen, Doctoral Dissertation, University of Heidelberg, 1972.

[009] [LPP] F. Lust-Piquard and G. Pisier, Non commutative Khintchine and Paley inequalities, Ark. Mat. 29 (1991), 241-260. | Zbl 0755.47029

[010] [V] D. Voiculescu, Symmetries of some reduced free product C*-algebras, in: Operator Algebras and Ergodic Theory, Lecture Notes in Math. 1132 (1985), 556-588.

[011] [VDN] D. Voiculescu, K. Dykema and A. Nica, Free Random Variables, AMS (1992).