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)

 
 

 

One dimensional perturbations of compact operators


Author: Harkrishan Vasudeva
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
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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

  • [1] H. Hochstadt, One dimensional perturbations of compact operators, Proc. Amer. Math. Soc. 37 (1973), 465-467. MR 46 #9779. MR 0310681 (46:9779)
  • [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.
  • [3] H. L. Vasudeva, Monotone matrix functions, Dissertation, University of California, Irvine, 1970.

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 47A55, 47B05

Retrieve articles in all journals with MSC: 47A55, 47B05


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1976-0445318-8
Article copyright: © Copyright 1976 American Mathematical Society

American Mathematical Society