Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

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

 
 

 

Finite rank perturbations of singular spectra


Author: James S. Howland
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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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

  • [1] R. Bouldin, On the perturbation of the singular spectrum, Pacific J. Math. 34 (1970), 569-583. MR 0268712 (42:3609)
  • [2] R. W. Carey and J. D. Pincus, Unitary equivalence modulo the trace class for selfadjoint operators, Amer. J. Math. 98 (1976), 481-514. MR 0420323 (54:8337)
  • [3] W. F. Donoghue, On the perturbation of spectra, Comm. Pure Appl. Math. 18 (1965), 559-579. MR 0190761 (32:8171)
  • [4] J. S. Howland, On a theorem of Aronszajn and Donoghue on singular spectra, Duke Math. J. 41 (1974), 141-143. MR 0333776 (48:12100)
  • [5] -, On the Kato-Rosemblum Theorem, Pacific J. Math. (to appear).
  • [6] T. Kato and S. T. Kuroda, The abstract theory of scattering, Rocky Mountain J. Math. 1 (1971), 127-171. MR 0385604 (52:6464b)
  • [7] -, Theory of simple scattering and eigenfunction expansions, Functional Analysis and Related Fields (F. Browder, ed.), Springer-Verlag, New York, 1970, pp. 99-131. MR 0385603 (52:6464a)

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

DOI: https://doi.org/10.1090/S0002-9939-1986-0845979-1
Article copyright: © Copyright 1986 American Mathematical Society

American Mathematical Society