Unitary groups and commutators
HTML articles powered by AMS MathViewer
- by Robert M. Kauffman PDF
- Proc. Amer. Math. Soc. 33 (1972), 95-100 Request permission
Abstract:
If H is a possibly unbounded selfadjoint operator and A is a closed operator in a Hilbert space, the relation $(U_t^{ - 1}A{U_t}f)’ = iU_t^{ - 1}(AH - HA){U_t}f$ can be shown to hold under relatively reasonable hypotheses on A and f, where ${U_t} = {e^{iHt}}$. This relation can then be used to relate properties of the commutator $AH - HA$ to properties of A and H.References
- Tosio Kato, Perturbation theory for linear operators, Die Grundlehren der mathematischen Wissenschaften, Band 132, Springer-Verlag New York, Inc., New York, 1966. MR 0203473
- Peter D. Lax and Ralph S. Phillips, Scattering theory, Pure and Applied Mathematics, Vol. 26, Academic Press, New York-London, 1967. MR 0217440
- C. R. Putnam, Commutation properties of Hilbert space operators and related topics, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 36, Springer-Verlag New York, Inc., New York, 1967. MR 0217618
Additional Information
- © Copyright 1972 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 33 (1972), 95-100
- MSC: Primary 47.40
- DOI: https://doi.org/10.1090/S0002-9939-1972-0290167-3
- MathSciNet review: 0290167