Geodesic
Change of Jordan structure of $G$-selfadjoint operators and selfadjoinl operator-functions under small perturbatios
Izvestiya. Mathematics , Tome 37 (1991) no. 2, pp. 371-395.

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

The author considers the problem of the change of length of Jordan chains when passing from $G_0$-selfadjoint operator $A_0$ to $G$-selfadjoint operator $A$, provided $\|A-A_0\|+\|G-G_0\|$ is small enough. The role played by the so-called sign characteristics is clarified. The results will carry over to the case of small perturbations of holomorphic selfadjoint operator-valued functions. 
@article{IM2_1991_37_2_a5,
     author = {V. R. Ol'shevskii},
     title = {Change of {Jordan} structure of $G$-selfadjoint operators and selfadjoinl operator-functions under small perturbatios},
     journal = {Izvestiya. Mathematics },
     pages = {371--395},
     publisher = {mathdoc},
     volume = {37},
     number = {2},
     year = {1991},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1991_37_2_a5/}
}
TY  - JOUR
AU  - V. R. Ol'shevskii
TI  - Change of Jordan structure of $G$-selfadjoint operators and selfadjoinl operator-functions under small perturbatios
JO  - Izvestiya. Mathematics 
PY  - 1991
SP  - 371
EP  - 395
VL  - 37
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IM2_1991_37_2_a5/
LA  - en
ID  - IM2_1991_37_2_a5
ER  - 
%0 Journal Article
%A V. R. Ol'shevskii
%T Change of Jordan structure of $G$-selfadjoint operators and selfadjoinl operator-functions under small perturbatios
%J Izvestiya. Mathematics 
%D 1991
%P 371-395
%V 37
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IM2_1991_37_2_a5/
%G en
%F IM2_1991_37_2_a5
V. R. Ol'shevskii. Change of Jordan structure of $G$-selfadjoint operators and selfadjoinl operator-functions under small perturbatios. Izvestiya. Mathematics , Tome 37 (1991) no. 2, pp. 371-395. http://geodesic.mathdoc.fr/item/IM2_1991_37_2_a5/

[1] Gohberg I., Kaashoek M. A., “Unsolved problems in matrix and operator theory. 1: Parti multiplicities and additive perturbations”, Integr. Equat. and Oper Theory, 1 (1978), 278–283 | DOI | MR | Zbl

[2] Markus A. S., Parilis E. E., “Ob izmenenii zhordanovoi struktury matritsy pri malykh vozmuscheniyakh”, Lineinye operatory, Kishinëv, 1980, 98–109 | MR | Zbl

[3] den Boer H., Thijsse G. Ph. A., “Semi-stability of sums of partial multiplicities under additve perturbation”, Integr. Equat. and Oper. Theory, 3 (1980), 23–42 | DOI | MR | Zbl

[4] Maltsev A. I., Osnovy lineinoi algebry, Nauka, M., 1975

[5] Gohberg I., Lancaster P., Rodman L., Matrices and indefinite scalar products, Birkhauser Verlag, Basel etc., 1983 | MR

[6] Keldysh M. V., “O polnote sobstvennykh funktsii nekotorykh klassov nesamosopryazhennykh lineinykh operatorov”, UMN, 26:4 (1971), 15–4 | MR | Zbl

[7] Kostyuchenko A. G., Shkalikov A. A., “Samosopryazhennye kvadratichnye puchki operatorov i ellipticheskie zadachi”, Funktsnon. analiz i ego prilozh., 17:2 (1983), 38–61 | MR | Zbl

[8] Ran A. C. M., Rodman L., “Stability of invariant maximal semidefinite subspaces, I”, Linear Algebra Appl., 62 (1984), 51–86 | DOI | MR | Zbl

[9] Olshevskii V. R., “Ob izmenenii zhordanovoi struktury $G$-samosopryazhennykh operatorov i samosopryazhennykh operator-funktsii pri malykh vozmuscheniyakh”, Funktsion. analiz i ego prilozh., 22:3 (1988), 79–80 | MR | Zbl

[10] Gantmakher F. R., Teoriya matrits, Nauka, M., 1966 | MR

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

[12] Glazman I. M., Lyubich Yu. I., Konechnomernyi lineinyi analiz v zadachakh, Nauka, M., 1969 | MR | Zbl

[13] Ran A. C. M., Rodman L., “Stability of invariant maximal semidefinite subspaces. II: Applications: selfadjoint rational matrix functions, algebraic Riccatti equations”, Linear Algebra Appl., 63 (1984), 51–86 | DOI | MR

[14] Markus A. S., “O golomorfnykh operator-funktsiyakh”, DAN SSSR, 119:6 (1958), 1099–1102 | MR | Zbl

[15] Kaashoek M. A., van der Mee C. V. M., Rodman L., “Analytic operator functions with compact spectrum. I: Spectral nodes, linearization and equivalence”, Integr. Equat. and Oper. Theory, 4 (1981), 504–547 | DOI | MR | Zbl

[16] Kaashoek M. A., van der Mee C. V. M., Rodman L., “Analytic operator functions with compact spectrum. II: Spectral pairs and factorization”, Integr. Equat. and Oper. Theory, 5 (1982), 791–829 | DOI | MR

[17] Kaashoek M. A., van der Mee C. V. M., Rodman L., “Analytic operator functions with compact spectrum. III: Hilbert space case: Inverse problem and applications”, J. of Oper. Theory, 10 (1983), 219–250 | MR | Zbl

[18] Pierce S., Rodman L., “Congruences and norms of hermitian matrices”, Canadian J. of Math., XXXIX:6 (1987), 1446–1458 | MR