Geodesic
Jordan operator algebras
Itogi Nauki i Tekhniki. Seriya Sovremennye Problemy Matematiki. Noveishie Dostizheniya, Tome 27 (1985), pp. 67-98.

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A survey of recent results in classification of $JW$-algebras (weakly closed Jordan algebras of self-adjoint operators in the Hilbert space) is given along with connections of $JW$-algebras with their enveloping $W^*$-algebras. It is shown how these results are applied in the proofs of analogs of many important results in the theory of $W^*$-algebras. 
@article{INTD_1985_27_a2,
     author = {Sh. A. Ayupov},
     title = {Jordan operator algebras},
     journal = {Itogi Nauki i Tekhniki. Seriya Sovremennye Problemy Matematiki. Noveishie Dostizheniya},
     pages = {67--98},
     publisher = {mathdoc},
     volume = {27},
     year = {1985},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTD_1985_27_a2/}
}
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Sh. A. Ayupov. Jordan operator algebras. Itogi Nauki i Tekhniki. Seriya Sovremennye Problemy Matematiki. Noveishie Dostizheniya, Tome 27 (1985), pp. 67-98. http://geodesic.mathdoc.fr/item/INTD_1985_27_a2/