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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Positive perturbations of unbounded operators
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by J. Dombrowski PDF
Proc. Amer. Math. Soc. 64 (1977), 287-290 Request permission

Abstract:

This work studies the spectral properties of certain unbounded selfadjoint operators by considering positive perturbations of such operators and the unitary equivalence of the perturbed and unperturbed transformations. Conditions are obtained on the unitary operators implementing this equivalence which guarantee that the selfadjoint operators have an absolutely continuous part.
References
  • Paul R. Halmos, Introduction to Hilbert space and the theory of spectral multiplicity, AMS Chelsea Publishing, Providence, RI, 1998. Reprint of the second (1957) edition. MR 1653399
  • Tosio Kato, Perturbation theory for linear operators, Die Grundlehren der mathematischen Wissenschaften, Band 132, Springer-Verlag New York, Inc., New York, 1966. MR 0203473
  • 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
  • C. R. Putnam, Positive perturbations and unitary equivalence, Canadian J. Math. 29 (1977), no. 1, 161–164. MR 430855, DOI 10.4153/CJM-1977-015-0
  • Marshall Harvey Stone, Linear transformations in Hilbert space, American Mathematical Society Colloquium Publications, vol. 15, American Mathematical Society, Providence, RI, 1990. Reprint of the 1932 original. MR 1451877, DOI 10.1090/coll/015
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Additional Information
  • © Copyright 1977 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 64 (1977), 287-290
  • MSC: Primary 47B25; Secondary 47A55
  • DOI: https://doi.org/10.1090/S0002-9939-1977-0448142-6
  • MathSciNet review: 0448142