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arXiv · 1509.08024

Unbounded operators in Hilbert space, duality rules, characteristic projections, and their applications

Palle Jorgensen·Erin Pearse·Feng Tian
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Abstract

Our main theorem is in the generality of the axioms of Hilbert space, and the theory of unbounded operators. Consider two Hilbert spaces such that their intersection contains a fixed vector space D. It is of interest to make a precise linking between such two Hilbert spaces when it is assumed that D is dense in one of the two; but generally not in the other. No relative boundedness is assumed. Nonetheless, under natural assumptions (motivated by potential theory), we prove a theorem where a comparison between the two Hilbert spaces is made via a specific selfadjoint semibounded operator. Applications include physical Hamiltonians, both continuous and discrete (infinite network models), and operator theory of reflection positivity.

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Palle Jorgensen, Erin Pearse, Feng Tian. 2015-09-26. Unbounded operators in Hilbert space, duality rules, characteristic projections, and their applications. https://arxiv.org/abs/1509.08024

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