Operator-valued Non-Commutative Probability and Analytic Functions, Part 1

David Jekel
University of California, Los Angeles (UCLA)

We give an introduction to operator-valued non-commutative probability spaces and laws. We discuss motivating examples, including conditional expectations and matrix amplifications of scalar-valued laws related to the linearization trick. We prove Williams' analytic characterization of the operator-valued Cauchy transform in terms of matricial analytic functions.

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