Unbounded Hermitian operators and relative reproducing kernel Hilbert space

• Autorzy: Palle Jorgensen
• Języki publikacji: EN

Abstrakty

EN

We study unbounded Hermitian operators with dense domain in Hilbert space. As is known, the obstruction for a Hermitian operator to be selfadjoint or to have selfadjoint extensions is measured by a pair of deficiency indices, and associated deficiency spaces; but in practical problems, the direct computation of these indices can be difficult. Instead, in this paper we identify additional structures that throw light on the problem. We will attack the problem of computing deficiency spaces for a single Hermitian operator with dense domain in a Hilbert space which occurs in a duality relation with a second Hermitian operator, often in the same Hilbert space.

Słowa kluczowe

EN

Hilbert space; Linear operator; Reproducing kernel; Function spaces

Kategorie tematyczne

• 47B37: Operators on special spaces (weighted shifts, operators on sequence spaces, etc.)
• 81Q10: Selfadjoint operator theory in quantum theory, including spectral analysis
• 81P15: Quantum measurement theory
• 47B32: Operators in reproducing-kernel Hilbert spaces (including de Branges, de Branges-Rovnyak, and other structured spaces)
• 47B25: Symmetric and selfadjoint operators (unbounded)
• 47S50: Operator theory in probabilistic metric linear spaces
• 60H25: Random operators and equations

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2010
• Tom: 8
• Numer: 3
• Strony: 569-596

Daty

wydano

2010-06-01

online

2010-05-30

Twórcy

autor

Palle Jorgensen

• The University of Iowa

Bibliografia

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Identyfikatory

DOI

10.2478/s11533-010-0021-8