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arXiv · 1504.07756

Dilations on locally Hilbert spaces

Dumitru Gaşpar·Păstorel Gaşpar·Nicolae Lupa
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Abstract

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.

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Dumitru Gaşpar, Păstorel Gaşpar, Nicolae Lupa. 2015-04-29. Dilations on locally Hilbert spaces. https://arxiv.org/abs/1504.07756

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