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arXiv · 1509.08853

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

Mihai Popa·Victor Vinnikov·Jiun-Chau Wang
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Abstract

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

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Mihai Popa, Victor Vinnikov, Jiun-Chau Wang. 2015-09-29. On the multiplication of operator-valued c-free random variables. https://arxiv.org/abs/1509.08853

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