Mathematische Annalen

, Volume 319, Issue 1, pp 1–16

Operator Khintchine inequality in non-commutative probability

  • Artur Buchholz
Original article

DOI: 10.1007/PL00004425

Cite this article as:
Buchholz, A. Math Ann (2001) 319: 1. doi:10.1007/PL00004425

Abstract. For the operator \(T=\sum^N_{k=1}A_K \otimes R_k\), where \(A_k\) belongs to the Schatten class \(S_{2n}\) and where \(R_k\) are non-commutative random variables with mixed moments satisfying a specific condition, we prove the following Khintchine inequality


We find the optimal constants \(D_{2n}\) in the case when \(R_{k}\) are the q-Gaussian and circular random variables. Moreover, we show that the moments of any probability symmetric measure appear as the optimal constants for some random variables.

Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Artur Buchholz
    • 1
  1. 1.Instytut Matematyczny, Uniwersytet Wrocławski, pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland (e-mail: PL