Geodesic
A perturbation characterization of compactness of self-adjoint operators
Heydar Radjavi1 ; Ping-Kwan Tam2 ; Kok-Keong Tan1
1Department of Mathematics and Statistics Dalhousie University Halifax, Nova Scotia, Canada, B3H 3J5
2Department of Mathematics Chinese University of Hong Kong Shatin, New Territories, Hong Kong
Studia Mathematica, Tome 158 (2003) no. 3, pp. 199-205
Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

Voir la notice de l'article

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.
DOI : 10.4064/sm158-3-1
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

Heydar Radjavi  1   ; Ping-Kwan Tam  2   ; Kok-Keong Tan  1

1 Department of Mathematics and Statistics Dalhousie University Halifax, Nova Scotia, Canada, B3H 3J5
2 Department of Mathematics Chinese University of Hong Kong Shatin, New Territories, Hong Kong 
@article{10_4064_sm158_3_1,
     author = {Heydar Radjavi and Ping-Kwan Tam and Kok-Keong Tan},
     title = {A perturbation characterization of compactness
 of self-adjoint operators},
     journal = {Studia Mathematica},
     pages = {199--205},
     year = {2003},
     volume = {158},
     number = {3},
     doi = {10.4064/sm158-3-1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/sm158-3-1/}
}
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
SP  - 199
EP  - 205
VL  - 158
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.4064/sm158-3-1/
DO  - 10.4064/sm158-3-1
LA  - en
ID  - 10_4064_sm158_3_1
ER  - 
%0 Journal Article
%A Heydar Radjavi
%A Ping-Kwan Tam
%A Kok-Keong Tan
%T A perturbation characterization of compactness
 of self-adjoint operators
%J Studia Mathematica
%D 2003
%P 199-205
%V 158
%N 3
%U http://geodesic.mathdoc.fr/articles/10.4064/sm158-3-1/
%R 10.4064/sm158-3-1
%G en
%F 10_4064_sm158_3_1
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

Cité par Sources :