L ∞ -Khintchine-Bonami inequality in free probability

Artur Buchholz

Banach Center Publications (1998)

  • Volume: 43, Issue: 1, page 105-109
  • ISSN: 0137-6934

Abstract

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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 | = l a w ⊗ λ ( w ) ). Next, we replace the translations by the free generators with a free family of operators and prove inequalities of the same type.

How to cite

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Buchholz, Artur. "$L_∞$-Khintchine-Bonami inequality in free probability." Banach Center Publications 43.1 (1998): 105-109. <http://eudml.org/doc/208829>.

@article{Buchholz1998,
abstract = {We prove the norm estimates for operator-valued functions on free groups supported on the words with fixed length ($f = ∑_\{|w| = l\} a_\{w\} ⊗ λ(w)$). Next, we replace the translations by the free generators with a free family of operators and prove inequalities of the same type.},
author = {Buchholz, Artur},
journal = {Banach Center Publications},
keywords = {Khintchine inequality; Rademacher functions; -Khintchine-Bonami inequalities; operator-valued functions},
language = {eng},
number = {1},
pages = {105-109},
title = {$L_∞$-Khintchine-Bonami inequality in free probability},
url = {http://eudml.org/doc/208829},
volume = {43},
year = {1998},
}

TY - JOUR
AU - Buchholz, Artur
TI - $L_∞$-Khintchine-Bonami inequality in free probability
JO - Banach Center Publications
PY - 1998
VL - 43
IS - 1
SP - 105
EP - 109
AB - We prove the norm estimates for operator-valued functions on free groups supported on the words with fixed length ($f = ∑_{|w| = l} a_{w} ⊗ λ(w)$). Next, we replace the translations by the free generators with a free family of operators and prove inequalities of the same type.
LA - eng
KW - Khintchine inequality; Rademacher functions; -Khintchine-Bonami inequalities; operator-valued functions
UR - http://eudml.org/doc/208829
ER -

References

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  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. Zbl0819.20043
  4. [Bn] A. Bonami, Étude des coefficients de Fourier des fonctions de L p ( G ) , Ann. Inst. Fourier 20,2 (1970), 335-402. Zbl0195.42501
  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. Zbl0377.46013
  7. [H2] U. Haagerup, An example of a non-nuclear C*-algebra which has the metric approximation property, Invent. Math. 50 (1979), 279-293. Zbl0408.46046
  8. [HP] U. Haagerup and G. Pisier, Bounded linear operators between C*-algebras, Duke Math. J. 71 (1993), 889-925. Zbl0803.46064
  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. Zbl0755.47029
  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). 

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