Download PDF - $L_∞$-Khintchine-Bonami inequality in free probabilityAll rights reserved. Copyright exceptions and limitations apply

ArticleOriginal scientific text

Title

L∞-Khintchine-Bonami inequality in free probability

Authors 1

Affiliations

  1. Institute of Mathematics, University of Wrocław, pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland

Abstract

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.

Bibliography

  1. [Bo1] M. Bożejko, On Λ(p) sets with minimal constant in discrete noncommutative groups, Proc. Amer. Math. Soc. 51(2) (1975), 407-412.
  2. [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.
  3. [BSp] M. Bożejko and R. Speicher, Completely positive maps on Coxeter groups, deformed commutation relations, and operator spaces, Math. Annalen 300 (1994), 97-120.
  4. [Bn] A. Bonami, Étude des coefficients de Fourier des fonctions de Lp(G), Ann. Inst. Fourier 20,2 (1970), 335-402.
  5. [Bu] A. Buchholz, Norm of convolution by operator-valued functions on free groups, To appear in Proc. Amer. Math. Soc.
  6. [H1] U. Haagerup, Les meilleures constantes de l'inégalité de Khintchine, C. R. Acad. Soc. Paris 286 (1978), A259-A262.
  7. [H2] U. Haagerup, An example of a non-nuclear C*-algebra which has the metric approximation property, Invent. Math. 50 (1979), 279-293.
  8. [HP] U. Haagerup and G. Pisier, Bounded linear operators between C*-algebras, Duke Math. J. 71 (1993), 889-925.
  9. [L] M. Leinert, Multiplikatoren diskreter Gruppen, Doctoral Dissertation, University of Heidelberg, 1972.
  10. [LPP] F. Lust-Piquard and G. Pisier, Non commutative Khintchine and Paley inequalities, Ark. Mat. 29 (1991), 241-260.
  11. [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.
  12. [VDN] D. Voiculescu, K. Dykema and A. Nica, Free Random Variables, AMS (1992).
Banach Center Publications
1998/43/1
Export to PBN, Opens in new tab
Pages:
105-109
Main language of publication
English
Published
1998
Exact and natural sciences