A duality theory for unbounded Hermitian operators in Hilbert space

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dc.creatorJorgensen, Palle E. T.
dc.date2009-04-10
dc.date.accessioned2026-07-07T13:02:27Z
dc.date.available2026-07-07T13:02:27Z
dc.descriptionWe develop a duality theory for 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. While duality considerations are a tested tool in mathematics, 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.
dc.description33 pages
dc.identifierhttps://arxiv.org/abs/0904.1699
dc.identifierhttp://arxiv.org/abs/0904.1699
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/226454
dc.subjectMathematical Physics
dc.subject47B25, 47B32, 47B37, 47S50, 60H25, 81P15, 81Q10
dc.titleA duality theory for unbounded Hermitian operators in Hilbert space
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