A perturbation characterization of compactness of self-adjoint operators

Heydar Radjavi, Ping-Kwan Tam, and Kok-Keong Tan. "A perturbation characterization of compactness of self-adjoint operators." Studia Mathematica 158.3 (2003): 199-205. <http://eudml.org/doc/284526>.

@article{HeydarRadjavi2003,
abstract = {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.},
author = {Heydar Radjavi, Ping-Kwan Tam, Kok-Keong Tan},
journal = {Studia Mathematica},
keywords = {compact operator, self-adjointness; spectrum; separability},
language = {eng},
number = {3},
pages = {199-205},
title = {A perturbation characterization of compactness of self-adjoint operators},
url = {http://eudml.org/doc/284526},
volume = {158},
year = {2003},
}

TY - JOUR
AU - Heydar Radjavi
AU - Ping-Kwan Tam
AU - Kok-Keong Tan
TI - A perturbation characterization of compactness of self-adjoint operators
JO - Studia Mathematica
PY - 2003
VL - 158
IS - 3
SP - 199
EP - 205
AB - 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.
LA - eng
KW - compact operator, self-adjointness; spectrum; separability
UR - http://eudml.org/doc/284526
ER -