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Proceedings of the American Mathematical Society

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

 
 

 

Finite-dimensional perturbations


Author: Horst Behncke
Journal: Proc. Amer. Math. Soc. 72 (1978), 82-84
MSC: Primary 47B15; Secondary 47A55
DOI: https://doi.org/10.1090/S0002-9939-1978-0503536-6
MathSciNet review: 503536
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Abstract: Let A be a normal operator on the Hilbert space $ \mathcal{H}$ and let B be an operator of finite rank, rank $ B = m$, such that $ A + B$ is normal. Moreover let E (resp. F) denote the spectral projections of A (resp. $ A + B$) for the set $ \{ \zeta \in {\mathbf{C}}\vert\vert\zeta - \lambda \vert \leqslant \alpha \} $. Then $ \dim \;E - m \leqslant \dim F \leqslant \dim E + m$.


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DOI: https://doi.org/10.1090/S0002-9939-1978-0503536-6
Keywords: Finite dimensional perturbations, normal operators
Article copyright: © Copyright 1978 American Mathematical Society

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