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On the multiplication of operator-valued c-free random variables

Volume 153 / 2018

Mihai Popa, Victor Vinnikov, Jiun-Chiau Wang Colloquium Mathematicum 153 (2018), 241-260 MSC: Primary 46L54; Secondary 05A15. DOI: 10.4064/cm7241-9-2017 Published online: 30 May 2018


The paper discusses some results concerning multiplication of non-commutative random variables that are c-free with respect to a pair $( \varPhi , \varphi ) $, where $ \varPhi $ is a linear map with values in some Banach algebra or C$^\ast $-algebra and $ \varphi $ is scalar-valued. In particular, we construct a suitable analogue of Voiculescu’s $ S $-transform for this framework.


  • Mihai PopaDepartment of Mathematics
    University of Texas at San Antonio
    One UTSA Circle
    San Antonio, TX 78249, U.S.A.
    “Simon Stoilow” Institute of Mathematics
    of the Romanian Academy
    P.O. Box 1-764
    014700 Bucureşti, Romania
  • Victor VinnikovDepartment of Mathematics
    Ben-Gurion University of the Negev
    Be’er Sheva 8410501, Israel
  • Jiun-Chiau WangDepartment of Mathematics and Statistics
    University of Saskatchewan
    Saskatoon, SK S7N 5E6, Canada

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