Class on “Non-Commutative Distributions”: Hand-Written Notes are Up

I have now put up scans of my hand-written notes for the class, see here, and will update those irregularly.

The class is still running well and more or less according to plan. After generalities on non-commutative distributions, non-commutative (fully matricial) functions, and operator-valued Cauchy transforms we are now bringing some structure into our non-commutative distributions, by looking on operator-valued freeness. I plan to cover the basic part of the theory of operator-valued freeness, in particular, operator-valued additive convolution, both from a combinatorial and an analytic point of view. However, much of this is parallel to the scalar-valued theory from last term, so I will be quite brief on details (in particular, proofs) at many places – one should look back to and compare with the relevant parts from last term; in particular, Sections 2, 3, 4, 5 of the corresponding class notes.

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