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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: Let $A$ and $B$ be semibounded (bounded from below) operators in a Hilbert space $\mathfrak H$ and $\mathfrak D$ a dense linear manifold contained in the domains of $AB$, $BA$, $A^2$, and $B^2$, and such that $ABx=BAx$ for all $x$ in $\mathfrak D$. It is shown that if the restriction of $(A+B)^2$ to $\mathfrak D$ is essentially self-adjoint, then $A$ and $B$ are essentially self-adjoint and $\bar A$ and $\bar B$ commute, i.e. their spectral projections permute.


References [Enhancements On Off] (What's this?)

  • 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

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