Geodesic
Invariant Subspaces of Dissipative Operators in a~Space with Indefinite Metric
Informatics and Automation, Studies on function theory and differential equations, Tome 248 (2005), pp. 294-303

Voir la notice de l'article provenant de la source Math-Net.Ru

A theorem on the existence of maximal nonnegative invariant subspaces is proved for a special class of dissipative operators in a Hilbert space with indefinite inner product. It is shown that the spectra of the restrictions of these operators on the corresponding invariant subspaces lie in the closed upper half-plane. The theorem obtained is a generalization of the well-known results of L. S. Pontryagin, H. K. Langer, M. G. Krein, and T. Ya. Azizov devoted to this subject. 
@article{TRSPY_2005_248_a26,
     author = {A. A. Shkalikov},
     title = {Invariant {Subspaces} of {Dissipative} {Operators} in {a~Space} with {Indefinite} {Metric}},
     journal = {Informatics and Automation},
     pages = {294--303},
     publisher = {mathdoc},
     volume = {248},
     year = {2005},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2005_248_a26/}
}
TY  - JOUR
AU  - A. A. Shkalikov
TI  - Invariant Subspaces of Dissipative Operators in a~Space with Indefinite Metric
JO  - Informatics and Automation
PY  - 2005
SP  - 294
EP  - 303
VL  - 248
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TRSPY_2005_248_a26/
LA  - ru
ID  - TRSPY_2005_248_a26
ER  - 
%0 Journal Article
%A A. A. Shkalikov
%T Invariant Subspaces of Dissipative Operators in a~Space with Indefinite Metric
%J Informatics and Automation
%D 2005
%P 294-303
%V 248
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TRSPY_2005_248_a26/
%G ru
%F TRSPY_2005_248_a26
A. A. Shkalikov. Invariant Subspaces of Dissipative Operators in a~Space with Indefinite Metric. Informatics and Automation, Studies on function theory and differential equations, Tome 248 (2005), pp. 294-303. http://geodesic.mathdoc.fr/item/TRSPY_2005_248_a26/