Unbounded operators in Hilbert space, duality rules, characteristic projections, and their applications
Functional Analysis
2017-01-19 v2
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.
Cite
@article{arxiv.1509.08024,
title = {Unbounded operators in Hilbert space, duality rules, characteristic projections, and their applications},
author = {Palle Jorgensen and Erin Pearse and Feng Tian},
journal= {arXiv preprint arXiv:1509.08024},
year = {2017}
}