One dimensional perturbations of compact operators
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- by Harkrishan Vasudeva
- Proc. Amer. Math. Soc. 57 (1976), 58-60
- DOI: https://doi.org/10.1090/S0002-9939-1976-0445318-8
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Abstract:
Let $A$ be a compact selfadjoint operator acting on a Hilbert space $H$. $P$ denotes a one dimensional projection also acting on $H$. It is shown that the eigenvalues of $A$ and $A + tP(t > 0)$ interlace on the real axis. A converse of this result is also proved.References
- Harry Hochstadt, One dimensional perturbations of compact operators, Proc. Amer. Math. Soc. 37 (1973), 465–467. MR 310681, DOI 10.1090/S0002-9939-1973-0310681-2 F. Riesz and B. Sz.-Nagy, Leçons d’analyse fonctionnelle, 2nd ed., Akad. Kiadó, Budapest, 1952; English transl., Ungar, New York, 1955, p. 234. MR 14, 286; 15, 132; 17, 175. H. L. Vasudeva, Monotone matrix functions, Dissertation, University of California, Irvine, 1970.
Bibliographic Information
- © Copyright 1976 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 57 (1976), 58-60
- MSC: Primary 47A55; Secondary 47B05
- DOI: https://doi.org/10.1090/S0002-9939-1976-0445318-8
- MathSciNet review: 0445318