Geodesic
On some general properties of metrical operators generated by quadratic operator pencils
Proceedings of the Yerevan State University. Physical and mathematical sciences, no. 2 (1987), pp. 3-8.

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

The article, which is a complementary one to the [3, 4], is devoted to the class of matrix operators generated by quadratic operator pencils. In terms of necessary and sufficient conditions on the elements of these matrices some theorems belonging to the known operator classes acting in usual Hilbert or indefinite Krein spaces have been formulated. Particularly, the necessary and sufficient conditions when the quadratic matrix operator is of Hilbert-Schmidt type or of nuclear type have been obtained. 
@article{UZERU_1987_2_a0,
     author = {G. V. Virabyan},
     title = {On some general properties of metrical operators generated by quadratic operator pencils},
     journal = {Proceedings of the Yerevan State University. Physical and mathematical sciences},
     pages = {3--8},
     publisher = {mathdoc},
     number = {2},
     year = {1987},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/UZERU_1987_2_a0/}
}
TY  - JOUR
AU  - G. V. Virabyan
TI  - On some general properties of metrical operators generated by quadratic operator pencils
JO  - Proceedings of the Yerevan State University. Physical and mathematical sciences
PY  - 1987
SP  - 3
EP  - 8
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/UZERU_1987_2_a0/
LA  - ru
ID  - UZERU_1987_2_a0
ER  - 
%0 Journal Article
%A G. V. Virabyan
%T On some general properties of metrical operators generated by quadratic operator pencils
%J Proceedings of the Yerevan State University. Physical and mathematical sciences
%D 1987
%P 3-8
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/UZERU_1987_2_a0/
%G ru
%F UZERU_1987_2_a0
G. V. Virabyan. On some general properties of metrical operators generated by quadratic operator pencils. Proceedings of the Yerevan State University. Physical and mathematical sciences, no. 2 (1987), pp. 3-8. http://geodesic.mathdoc.fr/item/UZERU_1987_2_a0/

[1] M. G. Krein, G. K. Langer, “O nekotorykh matematicheskikh printsipakh lineinoi teorii dempfirovannykh kolebanii kontinuumov”, Trudy Mezhdunarodnogo simpoziuma po primeneniyu teorii funktsii kompleksnogo peremennogo v mekhanike sploshnoi sredy, Nauka, M., 1965, 283–322 | MR

[2] P. Khalmosh, Gilbertovo prostranstvo v zadachakh, Mir, M., 1970 | MR | Zbl

[3] G. V. Virabyan, “O spektralnykh svoistvakh matrichnykh operatorov. I”, Uch. zapiski EGU, 1980, no. 2

[4] G. V. Virabyan, “O spektralnykh svoistvakh matrichnykh operatorov. II”, Uch. zapiski EGU, 1980, no. 3

[5] V. A. Trenogin, B. M. Pisarevskii, T. S. Soboleva, Zadachi i uprazhneniya po funktsionalnomu analizu, Nauka, M., 1984 | MR | Zbl