turkmath.org

In the 2004 article Type I Product Systems of Hilbert Modules Barreto et al. define the notion of a completely positive semidefinite kernel valued in the bounded mappings between preC*-algebras and prove a dilation theorem for such kernels, which is a useful result tool in proving many other results and also it generalizes Paschke's dilation theorem. In this talk we will state and prove a version of their theorem in the larger category of locally C*-algebras. Applications will be discussed as time permits.