Geodesic
Operators in Krein Space
Matematičeskie zametki, Tome 76 (2004) no. 3, pp. 324-334.

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

We study self-adjoint operators in Krein space. Our goal is to show that there is a relationship between the following classes of operators: operators with a compact “corner”, definitizable operators, operators of classes $(\mathbf H)$ and $\mathbf K(\mathbf H)$, and operators of class $D_\kappa^+$. 
@article{MZM_2004_76_3_a1,
     author = {T. Ya. Azizov and L. I. Sukhocheva and V. A. Shtraus},
     title = {Operators in {Krein} {Space}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {324--334},
     publisher = {mathdoc},
     volume = {76},
     number = {3},
     year = {2004},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2004_76_3_a1/}
}
TY  - JOUR
AU  - T. Ya. Azizov
AU  - L. I. Sukhocheva
AU  - V. A. Shtraus
TI  - Operators in Krein Space
JO  - Matematičeskie zametki
PY  - 2004
SP  - 324
EP  - 334
VL  - 76
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2004_76_3_a1/
LA  - ru
ID  - MZM_2004_76_3_a1
ER  - 
%0 Journal Article
%A T. Ya. Azizov
%A L. I. Sukhocheva
%A V. A. Shtraus
%T Operators in Krein Space
%J Matematičeskie zametki
%D 2004
%P 324-334
%V 76
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2004_76_3_a1/
%G ru
%F MZM_2004_76_3_a1
T. Ya. Azizov; L. I. Sukhocheva; V. A. Shtraus. Operators in Krein Space. Matematičeskie zametki, Tome 76 (2004) no. 3, pp. 324-334. http://geodesic.mathdoc.fr/item/MZM_2004_76_3_a1/

[1] Azizov T. Ya., Iokhvidov I. S., “Lineinye operatory v prostranstvakh s indefinitnoi metrikoi i ikh prilozheniya”, Itogi nauki i tekhniki. Matem. analiz, 17, VINITI, M., 1979, 113–205 | MR

[2] Azizov T. Ya., Iokhvidov I. S., Osnovy teorii lineinykh operatorov v prostranstvakh s indefinitnoi metrikoi, Nauka, M., 1986

[3] Bognar J., Indefinite Inner Product Spaces, Springer-Verlag, Berlin, 1974 | Zbl

[4] Sukhocheva L. I., “O svoistvakh operatorov klassa Helton'a”, Vestn. Voronezhskogo gos. un-ta. Ser. fiz., matem., 2001, no. 1, 120–123 | Zbl

[5] Shtraus V. A., “O strukture operatorov dvazhdy perestanovochnykh s operatorom klassa $\mathbf K(\mathbf H)$”, Ukr. matem. zh., 38:6 (1986), 805 | MR | Zbl

[6] Shtraus V. A., “O strukture semeistva kommutiruyuschikh $J$-samosopryazhennykh operatorov”, Ukr. matem. zh., 41:10 (1989), 1431–1433 | MR | Zbl

[7] Langer H., “Spectral functions of definitizable operators in Kreĭn spaces”, Lect. Notes in Math., 948, Springer-Verlag, Berlin–Heidelberg–New York, 1982, 1–46

[8] Azizov T. Ya., Strauss V. A., “Spectral decompositions for classes of self-adjoint and normal operators on Krein spaces”, Spectral Theory and its Applications, Proceedings. Theta, 2003, 45–67 | MR

[9] Jonas P., Langer H., “Compact perturbations of definitizable operators”, J. Operator Theory, 2 (1979), 63–77 | MR | Zbl

[10] Akhiezer N. I., Glazman I. M., Teoriya lineinykh operatorov v gilbertovom prostranstve, T. 1, Vischa shkola, Kharkov, 1977