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A new approach to subordination results in free probability. (English) Zbl 1142.46030

Summary: We show that the subordination results of D. Voiculescu and Ph. Biane can be deduced from a continuity property of fixed points for analytic functions.

MSC:

46L54 Free probability and free operator algebras
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References:

[1] H. Bercovici and D. Voiculescu, Free convolution of measures with unbounded support, Indiana Univ. Math. J. 42 (1993), 733–773. · Zbl 0806.46070 · doi:10.1512/iumj.1993.42.42033
[2] Ph. Biane, Processes with free increments, Math. Z. 227 (1998), 143–174. · Zbl 0902.60060 · doi:10.1007/PL00004363
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[10] D. Voiculescu, The coalgebra of the free difference quotient and free probability, Internat. Math. Res. Notices 2000, 79–106. · Zbl 0952.46038
[11] D. Voiculescu, Analytic subordination consequences of free Markovianity, Indiana Univ. Math. J. 51 (2002), 1161–1166. · Zbl 1040.46044 · doi:10.1512/iumj.2002.51.2252
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