**"****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.