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A Fock space model for addition and multiplication of c-free random variables


Author: Mihai Popa
Journal: Proc. Amer. Math. Soc. 142 (2014), 2001-2012
MSC (2010): Primary 46L54, 30H20
DOI: https://doi.org/10.1090/S0002-9939-2014-11786-2
Published electronically: February 27, 2014
MathSciNet review: 3182019
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Abstract: The paper presents a Fock space model suitable for construction of c-free algebras. Immediate applications are direct proofs for the properties of the c-free $ R$- and $ S$-transforms.


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Mihai Popa
Affiliation: Center for Advanced Studies in Mathematics, Ben Gurion University of the Negev, P. O. Box 653, Be’er Sheva 84105, Israel; and Institute of Mathematics “Simion Stoilow” of the Romanian Academy, P. O. Box 1-764, Bucharest, RO-70700, Romania
Address at time of publication: Department of Mathematics, The University of Texas at San Antonio, One UTSA Circle, San Antonio, Texas 78249-0664; and Institute of Mathematics “Simion Stoilow” of the Romanian Academy, P. O. Box 1-764, Bucharest, RO-70700, Romania
Email: Mihai.Popa@utsa.edu

DOI: https://doi.org/10.1090/S0002-9939-2014-11786-2
Keywords: Free independence, c-free independence, creation/annihilation operators, ${}^cR$- and ${}^cS$-transforms
Received by editor(s): February 17, 2011
Received by editor(s) in revised form: March 24, 2012
Published electronically: February 27, 2014
Communicated by: Marius Junge
Article copyright: © Copyright 2014 American Mathematical Society