Journal article
Off-diagonal terms in symmetric operators
Journal of mathematical physics, Vol.41(4), pp.2337-2349
04/2000
DOI: 10.1063/1.533242
Abstract
In this paper we provide a quantitative comparison of two obstructions for a given symmetric operator
S
with dense domain in Hilbert space H to be self-adjoint. The first one is the pair of deficiency spaces of von Neumann, and the second one is of more recent vintage; Let
P
be a projection in H. We say that it is smooth relative to
S
if its range is contained in the domain of
S.
We say that smooth projections
{P
i
}
i=1
∞
diagonalize
S
if (a)
(I−P
i
)SP
i
=0
for all
i,
and (b)
sup
i
P
i
=I.
If such projections exist, then
S
has a self-adjoint closure (i.e.,
S̄
has a spectral resolution), and so our second obstruction to self-adjointness is defined from smooth projections
P
i
with
(I−P
i
)SP
i
≠0.
We prove results both in the case of a single operator
S
and a system of operators.
Details
- Title: Subtitle
- Off-diagonal terms in symmetric operators
- Creators
- Palle E. T Jorgensen - University of Iowa
- Resource Type
- Journal article
- Publication Details
- Journal of mathematical physics, Vol.41(4), pp.2337-2349
- DOI
- 10.1063/1.533242
- ISSN
- 0022-2488
- eISSN
- 1089-7658
- Number of pages
- 13
- Language
- English
- Date published
- 04/2000
- Academic Unit
- Mathematics
- Record Identifier
- 9984240877802771
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