Abstract: Given a *-semigroup G, an action of it on a set X, and a Hilbert space H, we consider B(H)-valued kernels on X, that are invariant under the action of G on X. The problem is to decide when *-representations of G onto another Hilbert space K can be obtained out of here. This is a general problem that contains, as particular cases, different dilation theorems, starting with the classical dilation theorems of Naimark, Toeplitz kernels, Hankel kernels, dilation theorems of Sz.-Nagy and Stinespring, as well as some more recent interpretations of wavelets.
Date: Wednesday, March 27, 2013
Place: Mathematics Seminar Room, SA-141
Tea and cookies will be served before the seminar.