%0 Journal Article
%T Dilations on locally Hilbert spaces
%A Dumitru Ga£¿par
%A P£¿storel Ga£¿par
%A Nicolae Lupa
%J Mathematics
%D 2015
%I arXiv
%X The principal theorem of Sz.-Nagy on dilation of a positive definite Hilbert space operator valued function has played a central role in the development of the non-self-adjoint operator theory. In this paper we introduce the positive definiteness for locally Hilbert space operator valued kernels, we prove an analogue of the Sz.-Nagy dilation theorem and, as application, we obtain dilation results for locally contractions and locally $\rho$ - contractions as well as for locally semi-spectral measures.
%U http://arxiv.org/abs/1504.07756v1