"Representations of *-Semigroups Associated to Invariant Kernels with Values Continuously Adjointable Operators"
Abstract: We consider positive semidefinite kernels valued in the *-algebra of continuous and continuously adjointable operators on a VH-space (Vector Hilbert space in the sense of Loynes) and that are invariant under actions of *-semigroups. For such a kernel we obtain two necessary and sufficient boundedness conditions in order for there to exist *-representations of the underlying *-semigroup on a VH-space linearisation, equivalently, on a reproducing kernel VH-space. We exhibit several situations when the latter boundedness condition is automatically fulfilled.
Date: Wednesday, October 14, 2015
Place: Mathematics Seminar Room, SA-141
Tea and cookies will be served before the seminar.