Geodesic
$JW$-factors and antiautomorphisms of von~Neumann algebras
Izvestiya. Mathematics , Tome 26 (1986) no. 1, pp. 201-209.

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

The connection between $JW$-factors and their enveloping von Neumann algebras is studied for $JW$-factors not isomorphic to the Hermitian part of any von Neumann algebra. It is proved that these $JW$-factors are determined by an involutive $^*$-antiautomorphism of the enveloping von Neumann algebra. A classification of $JW$-factors of type III according to types III$_\lambda$, $0\leqslant\lambda\leqslant1$, is given, and the existence of each type is proved. It is shown that there are only two nonisomorphic $JW$-factors of type II$_1$ for which the enveloping von Neumann algebras are hyperfinite. Bibliography: 18 titles. 
@article{IM2_1986_26_1_a7,
     author = {Sh. A. Ayupov},
     title = {$JW$-factors and antiautomorphisms of {von~Neumann} algebras},
     journal = {Izvestiya. Mathematics },
     pages = {201--209},
     publisher = {mathdoc},
     volume = {26},
     number = {1},
     year = {1986},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1986_26_1_a7/}
}
TY  - JOUR
AU  - Sh. A. Ayupov
TI  - $JW$-factors and antiautomorphisms of von~Neumann algebras
JO  - Izvestiya. Mathematics 
PY  - 1986
SP  - 201
EP  - 209
VL  - 26
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IM2_1986_26_1_a7/
LA  - en
ID  - IM2_1986_26_1_a7
ER  - 
%0 Journal Article
%A Sh. A. Ayupov
%T $JW$-factors and antiautomorphisms of von~Neumann algebras
%J Izvestiya. Mathematics 
%D 1986
%P 201-209
%V 26
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IM2_1986_26_1_a7/
%G en
%F IM2_1986_26_1_a7
Sh. A. Ayupov. $JW$-factors and antiautomorphisms of von~Neumann algebras. Izvestiya. Mathematics , Tome 26 (1986) no. 1, pp. 201-209. http://geodesic.mathdoc.fr/item/IM2_1986_26_1_a7/

[1] Topping D., “Jordan algebras of self-adjoint operators”, Mem. Anrer. Math. Soc., 53 (1965), 1–48 | MR

[2] Stormer E., “Jordan algebras of type I”, Acta Math., 115 (1966), 165–284 | DOI | MR

[3] Stormer E., “Irreducible Jordan algebras of self-adjoint operators”, Trans. Amer. Math. Soc., 130 (1968), 153–166 | DOI | MR

[4] Ajupov Sh. A., “Extension of traces and type criterions for Jordan algebras of self- adjoint operators”, Math. Z., 181 (1982), 253–268 | DOI | MR | Zbl

[5] Ayupov Sh. A., “Modulyarnye iordanovy algebry samosopryazhennykh operatorov”, TMF, 53:1 (1982), 77–82 | MR | Zbl

[6] Stormer E., “On the Jordan structure of $C^*$-algebras”, Trans. Amer. Math. Soc., 120 (1965), 438–447 | DOI | MR

[7] Stormer E., “Real structure in the hyperfinite factor”, Duke Math. J., 47 (1980), 145–153 | DOI | MR

[8] Topping D., “An isomorphism invariant for spin factors”, Math. Mech., 15 (1966), 1055–1066 | MR

[9] Alfsen E. M., Hanche-Olsen H., Shultz F. W., “State spaces of $C^*$-algebras”, Acta Math., 144 (1980), 267–305 | DOI | MR | Zbl

[10] Alfsen E. M., Shultz F. W., Stormer E., “A Gelfand–Neumark theorem for Jordan algebras”, Advances in Math., 28 (1978), 11–56 | DOI | MR | Zbl

[11] Jacobson N., Structure and Representations of Jordan algebras, Amer. Math. Soc., Providence, R. I., 1968 | MR | Zbl

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

[13] Connes A., “Classification of injective factors”, Ann. of Math., 104 (1976), 73–115 | DOI | MR | Zbl

[14] Giordano T., Jones V., “Antiautomorphismes involutifs du facteur hyperfini de type $\operatorname{II_1}$”, C. R. Acad. Sci. Paris Sér. A-B, 290:1 (1980), 29–31 | MR | Zbl

[15] Giordano T., “Antiautomorphismes involutifs des facteurs injectifs”, C. R. Acad. Sci. Paris Sér. A, 291 (1980), 583–585 | MR | Zbl

[16] Connes A., “Outer conjugacy classes of automorphisms of factors”, Ann. scient. Ec. Norm. Sup., 8 (1975), 383–419 | MR | Zbl

[17] Stratila S., Modular theory in operator algebras, Editura Academiei and Abacus Press, 1981 | MR | Zbl

[18] Giordano T., Antiautomorphismes involutifs des facteurs de von Neumann injectifs, These, Neuchatel, 1981