Geodesic
Locally measurable operators for $JW$-algebras and the representation of ordered Jordan algebras
Izvestiya. Mathematics , Tome 24 (1985) no. 2, pp. 199-220.

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

The concept of local measurability is introduced for a selfadjoint operator with respect to a $JW$-algebra, and a theorem is proved on realization of ordered Jordan algebras of operators. Bibliography: 33 titles. 
@article{IM2_1985_24_2_a0,
     author = {Sh. A. Ayupov},
     title = {Locally measurable operators for $JW$-algebras and the representation of ordered {Jordan} algebras},
     journal = {Izvestiya. Mathematics },
     pages = {199--220},
     publisher = {mathdoc},
     volume = {24},
     number = {2},
     year = {1985},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1985_24_2_a0/}
}
TY  - JOUR
AU  - Sh. A. Ayupov
TI  - Locally measurable operators for $JW$-algebras and the representation of ordered Jordan algebras
JO  - Izvestiya. Mathematics 
PY  - 1985
SP  - 199
EP  - 220
VL  - 24
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IM2_1985_24_2_a0/
LA  - en
ID  - IM2_1985_24_2_a0
ER  - 
%0 Journal Article
%A Sh. A. Ayupov
%T Locally measurable operators for $JW$-algebras and the representation of ordered Jordan algebras
%J Izvestiya. Mathematics 
%D 1985
%P 199-220
%V 24
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IM2_1985_24_2_a0/
%G en
%F IM2_1985_24_2_a0
Sh. A. Ayupov. Locally measurable operators for $JW$-algebras and the representation of ordered Jordan algebras. Izvestiya. Mathematics , Tome 24 (1985) no. 2, pp. 199-220. http://geodesic.mathdoc.fr/item/IM2_1985_24_2_a0/

[1] Segal I. E., “A non commutative extension of abstract integration”, Ann. of Math., 57 (1953), 401–457 | DOI | MR | Zbl

[2] Sankaran S., “The ${}^*$-algebra of unbounded operators”, J. London Math. Soc., 34 (1959), 337–344 | DOI | MR | Zbl

[3] Sankaran S., “Stochastic convergence for operators”, Quart. J. Math. Oxford, Ser. 2, 15 (1964), 97–102 | DOI | MR | Zbl

[4] Yeadon F. J., “Convergence of measurable operators”, Proc. Camb. Phil. Soc., 74 (1973), 257–268 | DOI | MR | Zbl

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

[6] Sarymsakov T. A., Ayupov Sh. A., “Chastichno uporyadochennye iordanovy algebry”, DAN SSSR, 249:4 (1979), 789–792 | MR | Zbl

[7] Stormer E., “On the Jordan structure of $C^*$-algebras”, Trans. Amer. Mat. Soc., 120:12 (1965), 438–447 | DOI | MR

[8] Stormer E., “Jordan algebras of type I”, Acta Math., 115:3,4 (1966), 165–184 | DOI | MR

[9] Stormer E., “Irreducible Jordan algebras of self-adjoint operators”, Trans. Amer. Math. Soc., 130:1 (1968), 153–166 | DOI | MR

[10] Effros E. G., Stormer E., “Jordan algebras of self-adjoint operators”, Trans. Amer. Math. Soc., 127 (1967), 313–316 | DOI | MR | Zbl

[11] Effros E. G., Stormer E., “Positive projections and Jordan structure in operator algebras”, Math. Scand., 45:1 (1979), 127–138 | MR | Zbl

[12] Ajupov Sh. A., “Extension of traces and type criterions for Jordan algebras of selfadjoint operators”, Math. Z., 1982, no. 181, 253–268 | DOI | MR | Zbl

[13] Ayupov Sh. A., “K teorii chastichno uporyadochennykh iordanovykh algebr”, DAN UzSSR, 1979, no. 8, 6–8 | MR | Zbl

[14] Alfsen E. M., Shultz F. W., Stormer E., “A Gelfand–Neumark theorem for Jordan algebras”, Advances in Math., 28:1 (1978), 11–56 | DOI | MR | Zbl

[15] Ayupov Sh. A., “Integrirovanie na iordanovykh algebrakh”, Izv. AN SSSR. Seriya matem., 47:1 (1983), 3–25 | MR

[16] Ayupov Sh. A., “Uslovnye matematicheskie ozhidaniya i martingaly na iordanovykh algebrakh”, DAN UzSSR, 1981, no. 10, 3–5 | MR

[17] Ayupov Sh. A., “Statisticheskie ergodicheskie teoremy v iordanovykh algebrakh”, UMN, 36:6(222) (1981), 201–202 | MR | Zbl

[18] Ajupov S. A., “Probability spaces on Jordan algebras”, Third Int. Vilnius Conference on Probability Theory, Abstracts of Communications, v. III, 1981, 3–4

[19] Shultz F. W., “On normed Jordan algebras which are Banach dual spaces”, J. Functional Analysis, 31:3 (1979), 360–376 | DOI | MR | Zbl

[20] Ayupov Sh. A., Usmanov Sh. M., Poryadok i topologiya v iordanovykh algebrakh, DEP. VINITI No 4232-80 (RZh. Mat., 1981, No 1 A291) | Zbl

[21] Ayupov Sh. A., “$OJ$-algebry ogranichennykh elementov”, Izvestiya AN UzSSSR, seriya fiz.-mat. nauk, 1980, no. 2, 3–8 | MR

[22] Ayupov Sh. A., “Normalnye sostoyaniya na $OJB$-algebrakh”, Izvestiya AN UzSSR seriya fiz.-mat. nauk, 1980, no. 3, 9–13 | MR | Zbl

[23] Jordan P., von Neumann J., Wigner E., “On an algebrais generalization of the quantum mechanical formalism”, Ann. of Math., 35 (1934), 29–64 | DOI | MR | Zbl

[24] Stacey P. J., Type $I_2$ $JBW$-algebras, Preprint La Trobe University, 1980 | Zbl

[25] Zhevlakov K. A., Slinko A. M., Shestakov I. P., Shirshov A. I., Koltsa, blizkie k assotsiativnym, Nauka, M., 1978 | MR | Zbl

[26] Sarymsakov T. A., “Semifields and Probability Theory”, Lect. Notes Math., 550, 1976, 524–549 | MR | Zbl

[27] Antonovskii M. Ya., Boltyanskii V. G., Sarymsakov T. A., Topologicheskie algebry Bulya, AN UzSSR, Tashkent, 1963

[28] Sarymsakov T. A., Nosirov S. N., Khadzhiev Dzh., Opisanie idealov odnogo klassa kolets, DAN SSSR, 225, no. 5, 1975 | MR | Zbl

[29] Topping D. M., “Isomorphism invariant for spin factors”, J. Math. Mech., 15 (1966), 1055–1964 | MR

[30] Chilin V. I., “Berovskie uporyadochennye ${}^*$-algebry”, DAN SSSR, 258:5 (1981), 1065–1069 | MR

[31] Jacobson N., “Structure and Representations of Jordan algebras”, Amer. Math. Soc. Colloq. Publ., 39, Providence, RI, 1968 | MR | Zbl

[32] Takesaki M., Theory of Operator algebras, I, Springer-Verlag, New York, Heidelberg, Berlin, 1979 | MR

[33] Sakai S., $C^*$-algebras and $W^*$-algebras, Ergebnisse der Math., 60, Springer-Verlag, Berlin, 1971 | MR | Zbl