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On the S-transform over a Banach algebra

Kenneth J. Dykema
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Abstract

The S-transform is shown to satisfy a specific twisted multiplicativity property for free random variables in a B-valued Banach noncommutative probability space, for an arbitrary unital complex Banach algebra B. Also, a new proof of the additivity of the R-transform in this setting is given.

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Kenneth J. Dykema. 2005-01-11. On the S-transform over a Banach algebra. https://arxiv.org/abs/math/0501083

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