Complete commutative symmetric operator algebras in the Pontryagin space $\Pi_1$
Sbornik. Mathematics, Tome 13 (1971) no. 4, pp. 569-576 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

This paper describes, up to unitary equivalence, all (with the exception of simple cases considered previously) commutative subalgebras of all bounded operators on the Pontryagin space $\Pi_1$ which are closed in the uniform topology and contain along with each operator also its conjugate with respect to an indefinite scalar product. Bibliography: 6 titles.
@article{SM_1971_13_4_a4,
     author = {A. I. Loginov},
     title = {Complete commutative symmetric operator algebras in the {Pontryagin} space~$\Pi_1$},
     journal = {Sbornik. Mathematics},
     pages = {569--576},
     year = {1971},
     volume = {13},
     number = {4},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1971_13_4_a4/}
}
TY  - JOUR
AU  - A. I. Loginov
TI  - Complete commutative symmetric operator algebras in the Pontryagin space $\Pi_1$
JO  - Sbornik. Mathematics
PY  - 1971
SP  - 569
EP  - 576
VL  - 13
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/SM_1971_13_4_a4/
LA  - en
ID  - SM_1971_13_4_a4
ER  - 
%0 Journal Article
%A A. I. Loginov
%T Complete commutative symmetric operator algebras in the Pontryagin space $\Pi_1$
%J Sbornik. Mathematics
%D 1971
%P 569-576
%V 13
%N 4
%U http://geodesic.mathdoc.fr/item/SM_1971_13_4_a4/
%G en
%F SM_1971_13_4_a4
A. I. Loginov. Complete commutative symmetric operator algebras in the Pontryagin space $\Pi_1$. Sbornik. Mathematics, Tome 13 (1971) no. 4, pp. 569-576. http://geodesic.mathdoc.fr/item/SM_1971_13_4_a4/

[1] M. A. Naimark, “O kommutativnykh algebrakh operatorov v prostranstve $\Pi_1$”, DAN SSSR, 156:4 (1964), 734–737 | MR

[2] M. A. Naimark, “Kommutativnye algebry operatorov v prostranstve $\Pi_1$”, Rev. Roum. Math, Pures et Appl., 9:6 (1964), 499–529 | MR

[3] A. I. Loginov, “Banakhovy kommutativnye simmetrichnye algebry operatorov v prostranstve Pontryagina $\Pi_1$”, DAN SSSR, 179:6 (1968), 1276–1278 | MR | Zbl

[4] I. S. Iokhvidov, M. G. Krein, “Spektralnaya teoriya operatorov v prostranstvakh s indefinitnoi metrikoi”, Trudy Mosk. matem. ob-va, 5 (1956), 367–432 | MR

[5] M. A. Naimark, S. V. Fomin, “Nepreryvnye summy gilbertovykh prostranstv i nekotorye ikh primeneniya”, Uspekhi matem. nauk, X:2(64) (1955), 111–142 | MR

[6] M. A. Naimark, Normirovannye koltsa, Nauka, Moskva, 1968 | MR | Zbl