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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
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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.


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