Geodesic
Von Neumann $J$-Algebras in a Space with Two Symmetries
Matematičeskie zametki, Tome 82 (2007) no. 2, pp. 232-241

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We show that a von Neumann $J$-algebra $\mathscr A$ of type $(\mathrm B)$ does not contain $J$-positive ($J$-negative) operators. $J$-projections in $\mathscr A$ are characterized. The class of plus-operators that are simultaneously self-adjoint and $J$-self-adjoint is described.
Keywords: von Neumann algebra, indefinite metric, plus-operator, $J$-algebra, Hilbert space, polar decomposition of an operator. 
@article{MZM_2007_82_2_a7,
     author = {M. S. Matveichuk},
     title = {Von {Neumann} $J${-Algebras} in a {Space} with {Two} {Symmetries}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {232--241},
     publisher = {mathdoc},
     volume = {82},
     number = {2},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2007_82_2_a7/}
}
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M. S. Matveichuk. Von Neumann $J$-Algebras in a Space with Two Symmetries. Matematičeskie zametki, Tome 82 (2007) no. 2, pp. 232-241. http://geodesic.mathdoc.fr/item/MZM_2007_82_2_a7/