Journal article
Unbounded operators in Hilbert space, duality rules, characteristic projections, and their applications
Analysis and mathematical physics, Vol.8(3), pp.351-382
09/01/2018
DOI: 10.1007/s13324-017-0173-9
Abstract
Our main theorem is in the generality of the axioms of Hilbert space, and the theory of unbounded operators. Consider two Hilbert spaces whose intersection contains a fixed vector space . In the case when is dense in one of the Hilbert spaces (but not necessarily in the other), we make precise an operator-theoretic linking between the two Hilbert spaces. 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 the operator theory of reflection positivity.
Details
- Title: Subtitle
- Unbounded operators in Hilbert space, duality rules, characteristic projections, and their applications
- Creators
- Palle Jorgensen - Univ Iowa, Dept Math, Iowa City, IA 52242 USAErin Pearse - Calif Polytech State Univ San Luis Obispo, Dept Math, San Luis Obispo, CA 93407 USAFeng Tian - Hampton University
- Resource Type
- Journal article
- Publication Details
- Analysis and mathematical physics, Vol.8(3), pp.351-382
- Publisher
- SPRINGER BASEL AG
- DOI
- 10.1007/s13324-017-0173-9
- ISSN
- 1664-2368
- eISSN
- 1664-235X
- Number of pages
- 32
- Language
- English
- Date published
- 09/01/2018
- Academic Unit
- Mathematics
- Record Identifier
- 9984240763802771
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