Geodesic
On ideal of compact operators in real factors
Vladikavkazskij matematičeskij žurnal, Tome 6 (2004) no. 1, pp. 42-45 
A. A. Rakhimov; A. A. Katz; R. Dadakhodjaev. On ideal of compact operators in real factors. Vladikavkazskij matematičeskij žurnal, Tome 6 (2004) no. 1, pp. 42-45. http://geodesic.mathdoc.fr/item/VMJ_2004_6_1_a6/
@article{VMJ_2004_6_1_a6,
     author = {A. A. Rakhimov and A. A. Katz and R. Dadakhodjaev},
     title = {On ideal of compact operators in real factors},
     journal = {Vladikavkazskij matemati\v{c}eskij \v{z}urnal},
     pages = {42--45},
     year = {2004},
     volume = {6},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/VMJ_2004_6_1_a6/}
}
TY  - JOUR
AU  - A. A. Rakhimov
AU  - A. A. Katz
AU  - R. Dadakhodjaev
TI  - On ideal of compact operators in real factors
JO  - Vladikavkazskij matematičeskij žurnal
PY  - 2004
SP  - 42
EP  - 45
VL  - 6
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/VMJ_2004_6_1_a6/
LA  - en
ID  - VMJ_2004_6_1_a6
ER  - 
%0 Journal Article
%A A. A. Rakhimov
%A A. A. Katz
%A R. Dadakhodjaev
%T On ideal of compact operators in real factors
%J Vladikavkazskij matematičeskij žurnal
%D 2004
%P 42-45
%V 6
%N 1
%U http://geodesic.mathdoc.fr/item/VMJ_2004_6_1_a6/
%G en
%F VMJ_2004_6_1_a6

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

In the present paper the real ideals of relatively compact operators of $W^*$-algebras are considered. A description (up to isomorphism) of real two-sided ideal of relatively compact operators of the complex $W^*$-factors is given.

[1] Ajupov Sh. A., Rakhimov A. A., Usmanov Sh. M., Jordan real and Li structures in operator algebras, Kluwer, Dordrecht, 2001, 225 pp.

[2] Breuer M., “Fredholm theories in von Neumann algebras, I”, Math. Ann., 178 (1968), 243–254 | DOI | MR | Zbl

[3] Connes A., “Une classification des facteurs de type III”, Ann. Sc. Ec. Norm. Sup., 6 (1973), 133–252 | MR | Zbl

[4] Halpern H., Kaftal V., “Compact operators in type III$_{\lambda}$ and type III$_{0}$ factors”, Math. Ann., 273 (1986), 251–270 | DOI | MR | Zbl

[5] Rakhimov A. A., Katz A. A., Dadakhodjaev R., “The ideal of compact operators in real factors of types I and II”, Mat. Tr., 5:1 (2002), 129–134 (in Russian) | MR | Zbl

[6] Sonis M. G., “On a class of operators in von Neumann algebras with Segal measures”, Math. USSR Sb., 13 (1971), 344–359 | DOI | Zbl

[7] Stacey P. J., “Real structure in $\sigma$-finite factors of type III$_{\lambda }$, where $0\lambda 1$”, Proc. London Math. Soc. 3, 47 (1983), 275–284 | DOI | MR | Zbl