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Kunal Mukherjee
Indian Institute of Technology Madras
Noncommutative Joinings
Tuesday, November 17 1pm, 646 PGH
Abstract
We extend the classical theory of joinings of measurable dynamical systems to the noncommutative setting from interconnected points of view.
Among these is a particularly fruitful identification of joinings with equivariant quantum channels between
W*-dynamical systems that provides noncommutative generalizations of many results of classical joining theory.
We obtain fully general analogues of the main classical disjointness characterizations of ergodicity, primeness and (weak) mixing phenomena.
Our approach to the characterization of weak mixing yields that any finite dimensional invariant subspace of the induced unitary representation of a state preserving ergodic action of a group on the standard Hilbert space lies inside the image of the centralizer.
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Last modified: April 08 2016 - 07:21:37