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arXiv · 1712.02465

Free-Boolean independence with amalgamation

Weihua Liu·Ping Zhong
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Abstract

In this paper, we develop the notion of free-Boolean independence in an amalgamation setting. We construct free-Boolean cumulants and show that the vanishing of mixed free-Boolean cumulants is equivalent to our free-Boolean independence with amalgamation. We also provide a characterization of free-Boolean independence by conditions in terms of mixed moments. In addition, we study free-Boolean independence over a $C^*$-algebra and prove a positivity property.

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Weihua Liu, Ping Zhong. 2017-12-07. Free-Boolean independence with amalgamation. https://arxiv.org/abs/1712.02465

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