News & Events

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:
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.