"A General Dilation Theorem in VH-Spaces"
By
SERDAR AY
(BİLKENT UNIVERSITY)
Abstract: We prove a general dilation theorem for
positive semidefinite kernels that are invariant
under actions of $*$-semigroups and take values continuous
and continuously adjointable operators on a VH-space
(Vector Hilbert space in the sense of Loynes). This
theorem points out two necessary and sufficient conditions for the existence of
$*$-representations of the given $*$-semigroup on
VH-spaces or, equivalently, on reproducing kernel VH-spaces and it unifies many
known dilation theorems, including the recent dilation theorems in Hilbert modules
over $C^*$-algebras or locally $C^*$-algebras.
Date: Monday, March 2, 2015
Time: 14:40
Place: Mathematics Seminar Room, SA-141
Tea and cookies will be served before the
seminar.