Geodesic
The Ideal of Compact Operators in Real Factors of Types I and II
Matematičeskie trudy, Tome 5 (2002) no. 1, pp. 129-134 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

In the article we study the ideal of relatively compact operators in a real von Neumann factor. We prove a real analog of the Calkin theorem on the uniform closure and uniqueness of the ideal of relatively compact operators. In addition, we show that, unlike complex factors, in a real semifinite factor, up to isomorphism, there exist, in the discrete case, three, and, in the continuous case, two nonzero uniformly closed two-sided real ideals. 
@article{MT_2002_5_1_a8,
     author = {A. A. Rakhimov and A. A. Kats and R. A. Dadakhodjaev},
     title = {The~Ideal of {Compact} {Operators} in {Real} {Factors} of {Types~I} {and~II}},
     journal = {Matemati\v{c}eskie trudy},
     pages = {129--134},
     year = {2002},
     volume = {5},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MT_2002_5_1_a8/}
}
TY  - JOUR
AU  - A. A. Rakhimov
AU  - A. A. Kats
AU  - R. A. Dadakhodjaev
TI  - The Ideal of Compact Operators in Real Factors of Types I and II
JO  - Matematičeskie trudy
PY  - 2002
SP  - 129
EP  - 134
VL  - 5
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/MT_2002_5_1_a8/
LA  - ru
ID  - MT_2002_5_1_a8
ER  - 
%0 Journal Article
%A A. A. Rakhimov
%A A. A. Kats
%A R. A. Dadakhodjaev
%T The Ideal of Compact Operators in Real Factors of Types I and II
%J Matematičeskie trudy
%D 2002
%P 129-134
%V 5
%N 1
%U http://geodesic.mathdoc.fr/item/MT_2002_5_1_a8/
%G ru
%F MT_2002_5_1_a8
A. A. Rakhimov; A. A. Kats; R. A. Dadakhodjaev. The Ideal of Compact Operators in Real Factors of Types I and II. Matematičeskie trudy, Tome 5 (2002) no. 1, pp. 129-134. http://geodesic.mathdoc.fr/item/MT_2002_5_1_a8/

[1] Ovchinnikov V. I., “O $s$-chislakh izmerimykh operatorov”, Funktsionalnyi analiz i ego prilozheniya, 4:4 (1970), 78–85 | MR | Zbl

[2] Sonis M. G., “Ob odnom klasse operatorov v algebrakh fon Neimana s meroi Sigala na proektorakh”, Mat. sb., 84(126):3 (1970), 353–368

[3] Ayupov Sh. A., Rakhimov A. A., Usmanov Sh. M., Jordan, Real and Lie Structures in Operator Algebras, Math. Appl., 418, Kluwer Academic Publishers, Dordrecht, 1997 | MR | Zbl

[4] Kaftal V., “On the theory of compact operators in von Neumann algebras. I”, Indiana Univ. Math. J., 26:3 (1977), 447–457 | DOI | MR | Zbl

[5] Halpern H., Kaftal V., “Compact operators in type III$_\lambda$ and type III$_0$ factors”, Math. Ann., 273 (1986), 251–270 | DOI | MR | Zbl