A commutativity theorem for semibounded operators in hilbert space
Author:
A. Edward Nussbaum
Journal:
Proc. Amer. Math. Soc. 125 (1997), 3541-3545
MSC (1991):
Primary 47B25
DOI:
https://doi.org/10.1090/S0002-9939-97-03977-4
MathSciNet review:
1402881
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Abstract | References | Similar Articles | Additional Information
Abstract: Let and
be semibounded (bounded from below) operators in a Hilbert space
and
a dense linear manifold contained in the domains of
,
,
, and
, and such that
for all
in
. It is shown that if the restriction of
to
is essentially self-adjoint, then
and
are essentially self-adjoint and
and
commute, i.e. their spectral projections permute.
- 1. B. Fuglede, Conditions for two self-adjoint operators to commute or to satisfy the Weyl relation, Math. Scan. 51 (1982), 163-178. MR 84a:81013
- 2. T. Kato, Perturbation Theory for Linear Operators, Springer-Verlag, New York, 1966. MR 34:3324
- 3. E. Nelson, Analytic Vectors, Annals of Mathematics 70 (1959). MR 21:5901
- 4. M. Reed and B. Simon, Functional Analysis in Methods of Modern Mathematical Physics I, Academic Press, New York and London, 1972. MR 58:12429a
- 5. A. E. Nussbaum, A commutativity theorem for unbounded operators in Hilbert space, Trans. Amer. Math. Soc. 140 (1969), 485-491. MR 39:3345
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Additional Information
A. Edward Nussbaum
Affiliation:
Department of Mathematics, Washington University, St. Louis, Missouri 63130
Email:
addi@math.wustl.edu
DOI:
https://doi.org/10.1090/S0002-9939-97-03977-4
Received by editor(s):
April 30, 1996
Dedicated:
Dedicated to Allen Devinatz
Communicated by:
Palle E. T. Jorgensen
Article copyright:
© Copyright 1997
American Mathematical Society