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A new proof for the multiplicative property of the boolean cumulants with applications to the operator-valued case

Tom 117 / 2009

Mihai Popa Colloquium Mathematicum 117(2009), 81-93 MSC: 45L53, 46L08. DOI: 10.4064/cm117-1-5


The paper presents several combinatorial properties of the boolean cumulants. A consequence is a new proof of the multiplicative property of the boolean cumulant series that can be easily adapted to the case of boolean independence with amalgamation over an algebra.


  • Mihai PopaDepartment of Mathematics
    Indiana University at Bloomington
    Rawles Hall
    931 E 3rd St
    Bloomington, IN 47405, U.S.A.
    Institute of Mathematics
    Romanian Academy
    P.O. Box 1-764
    RO-70700, Bucureşti, Romania

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