Skip to Main Content

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.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Finite rank perturbations of singular spectra
HTML articles powered by AMS MathViewer

by James S. Howland PDF
Proc. Amer. Math. Soc. 97 (1986), 634-636 Request permission

Abstract:

Let $T$ be selfadjoint, and $V$ nonnegative of finite rank, with the range of $V$ cyclic for $T$. Then the singular parts of $T$ and $H = T + V$ are supported on two sets ${S_T}$ and ${S_H}$ such that the multiplicity of $T$ on ${S_T} \cap {S_H}$ is less than the rank of $V$.
References
  • Richard Bouldin, The peturbation of the singular spectrum, Pacific J. Math. 34 (1970), 569–583. MR 268712
  • R. W. Carey and J. D. Pincus, Unitary equivalence modulo the trace class for self-adjoint operators, Amer. J. Math. 98 (1976), no. 2, 481–514. MR 420323, DOI 10.2307/2373898
  • William F. Donoghue Jr., On the perturbation of spectra, Comm. Pure Appl. Math. 18 (1965), 559–579. MR 190761, DOI 10.1002/cpa.3160180402
  • James S. Howland, On a theorem of Aronszajn and Donoghue on singular spectra, Duke Math. J. 41 (1974), 141–143. MR 333776
  • —, On the Kato-Rosemblum Theorem, Pacific J. Math. (to appear).
  • Tosio Kato and S. T. Kuroda, Theory of simple scattering and eigenfunction expansions, Functional Analysis and Related Fields (Proc. Conf. for M. Stone, Univ. Chicago, Chicago, Ill., 1968) Springer, New York, 1970, pp. 99–131. MR 0385603
  • Tosio Kato and S. T. Kuroda, Theory of simple scattering and eigenfunction expansions, Functional Analysis and Related Fields (Proc. Conf. for M. Stone, Univ. Chicago, Chicago, Ill., 1968) Springer, New York, 1970, pp. 99–131. MR 0385603
Similar Articles
  • Retrieve articles in Proceedings of the American Mathematical Society with MSC: 47A55, 15A18
  • Retrieve articles in all journals with MSC: 47A55, 15A18
Additional Information
  • © Copyright 1986 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 97 (1986), 634-636
  • MSC: Primary 47A55; Secondary 15A18
  • DOI: https://doi.org/10.1090/S0002-9939-1986-0845979-1
  • MathSciNet review: 845979