A perturbation characterization of compactness
of self-adjoint operators
Studia Mathematica, Tome 158 (2003) no. 3, pp. 199-205
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
A characterization of compactness of a given self-adjoint bounded operator $A$ on a separable infinite-dimensional Hilbert space is established in terms of the spectrum of perturbations. An example is presented to show that without separability, the perturbation condition, which is always necessary, is not sufficient. For non-separable spaces, another condition on the self-adjoint operator $A$, which is necessary and sufficient for the perturbation, is given.
Keywords:
characterization compactness given self adjoint bounded operator separable infinite dimensional hilbert space established terms spectrum perturbations example presented without separability perturbation condition which always necessary sufficient non separable spaces another condition self adjoint operator which necessary sufficient perturbation given
Affiliations des auteurs :
Heydar Radjavi 1 ; Ping-Kwan Tam 2 ; Kok-Keong Tan 1
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author = {Heydar Radjavi and Ping-Kwan Tam and Kok-Keong Tan},
title = {A perturbation characterization of compactness
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journal = {Studia Mathematica},
pages = {199--205},
publisher = {mathdoc},
volume = {158},
number = {3},
year = {2003},
doi = {10.4064/sm158-3-1},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/sm158-3-1/}
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Heydar Radjavi; Ping-Kwan Tam; Kok-Keong Tan. A perturbation characterization of compactness of self-adjoint operators. Studia Mathematica, Tome 158 (2003) no. 3, pp. 199-205. doi: 10.4064/sm158-3-1
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