Geodesic
Von Neumann $J$-Algebras in a Space with Two Symmetries
Matematičeskie zametki, Tome 82 (2007) no. 2, pp. 232-241 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

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},
     year = {2007},
     volume = {82},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2007_82_2_a7/}
}
TY  - JOUR
AU  - M. S. Matveichuk
TI  - Von Neumann $J$-Algebras in a Space with Two Symmetries
JO  - Matematičeskie zametki
PY  - 2007
SP  - 232
EP  - 241
VL  - 82
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/MZM_2007_82_2_a7/
LA  - ru
ID  - MZM_2007_82_2_a7
ER  - 
%0 Journal Article
%A M. S. Matveichuk
%T Von Neumann $J$-Algebras in a Space with Two Symmetries
%J Matematičeskie zametki
%D 2007
%P 232-241
%V 82
%N 2
%U http://geodesic.mathdoc.fr/item/MZM_2007_82_2_a7/
%G ru
%F MZM_2007_82_2_a7
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/

[1] T. Ya. Azizov, I. S. Iokhvidov, Osnovy teorii lineinykh operatorov v prostranstvakh s indefinitnoi metrikoi, Nauka, M., 1986 | MR | Zbl

[2] M. M. Meltser, “O klassifikatsii $J$-algebr Neimana”, Funkts. analiz i ego pril., 13:4 (1979), 83–84 | MR

[3] M. S. Matvejchuk, “Probability masure in $W^*J$-algebras in Hilbert spaces with conjugation”, Proc. Amer. Math. Soc., 126:4 (1998), 1155–1164 | DOI | MR | Zbl