Dilations on Hilbert locally C^* - modules
by
Dumitru Gaspar
West University of Timisoara
Coauthors: Pastorel Gaspar

The numerous extensions of the famous dilation theorem of B. Sz.-Nagy are known in the mathematical literature of the last decades. We only recall the extension of this theorem to the dilation of Hilbert C^* modules operators given by S. Itoh.
It is the aim of this paper to obtain a Sz.-Nagy type dilation theorem in the context of Hilbert locally C^* - modules, which often appear in the study of operator algebras.
For this purpose the authos introduced and studied the positive defniteness for locally C^* - algebra valued kernels and the corresponding boundedness condition as well as the reproducing kernel Hilbert locally C^* - modules with their basic properties.
Then a Sz.-Nagy dilation theorem for operator positive definite function on a semigroup satsifying an appropiate boundedness condition is proved and finally many applications to operators semigroups on such Hilbert modules are obtained.

Date received: June 15, 2008