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Seminar by K. Mukherjee

Date/Time: 
Thursday, November 16, 2017 - 16:00 to 17:15
Venue: 
SMS SEMINAR HALL
Speaker: 
Dr. Kunal Krishna Mukherjee
Affiliation: 
IIT Madras
Title: 
On dynamical system preserving weights

The canonical unitary representation of a locally compact separable group arising from an ergodic action of the group on a von Neumann algebra with separable predual preserving a faithful normal semifinite (infinite) weight is weak mixing. On the contrary, there exists a non-ergodic automorphism of a von Neumann algebra preserving a faithful normal semifinite trace such that the spectral measure and the spectral multiplicity of the induced action are respectively the Haar measure (on the unit circle) and $\infty$. Despite not even being ergodic, this automorphism has the same spectral data as that of a Bernoulli shift.

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