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

18 Jan 2017  ·  Jorgensen Palle, Pearse Erin, Tian Feng ·

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. read more

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Functional Analysis