Event Details

Are four symmetries are enough?

Self-adjoint unitary operators on a Hilbert space are known as symmetries. Such operators have a very simple structure, with a spectrum contained in the two-point set {-1, 1}. In 1958 Halmos and Kakutani showed that every unitary operator on an infinite dimensional complex Hilbert space is a product of four symmetries. We show that in a von Neumann algebra of Type II every unitary is a product of six symmetries and that there are unitaries requiring four symmetries for such a decomposition.

The talk is intended to be accessible to PhD students; it is based on joint work with Soumyashant Nayak and P. Shankar.