Mathematische Zeitschrift

, Volume 253, Issue 1, pp 177–196

Remarks on the r and Δ convolutions

  • Marek Bożejko
  • Anna Dorota Krystek
  • Łukasz Jan Wojakowski
Article

DOI: 10.1007/s00209-005-0898-2

Cite this article as:
Bożejko, M., Krystek, A. & Wojakowski, Ł. Math. Z. (2006) 253: 177. doi:10.1007/s00209-005-0898-2
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Abstract

In this paper we study the properties of the r–deformation introduced in [B1]. We observe that the associated convolution coming from the conditionally free convolution is associative only for r = 1 and r = 0. We give the realization of some r–Gaussian random variables and obtain Haagerup–Pisier–Buchholz type inequalities. We also study another convolution defined with the use of the r–deformation through a moment–cumulant formula [KY1] and show that it is associative and in general not positive.

Keywords

Convolutionconditionally freefree and boolean convolutiondeformationsmoment–cumulant formulaelimit theoremsoperator spaces

Mathematics Subject Classification (2000)

Primary: 46L5346L54Secondary: 60E10

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Marek Bożejko
    • 1
  • Anna Dorota Krystek
    • 1
  • Łukasz Jan Wojakowski
    • 1
  1. 1.Mathematical InstituteUniversity of WrocławWrocławPoland