Geodesic
Field algebras in quantum theory with indefinite metric. II. Formulation of a modular theory in Pontryagin space
Teoretičeskaâ i matematičeskaâ fizika, Tome 62 (1985) no. 1, pp. 30-44 
K. Yu. Dadashyan; S. S. Horuzhy. Field algebras in quantum theory with indefinite metric. II. Formulation of a modular theory in Pontryagin space. Teoretičeskaâ i matematičeskaâ fizika, Tome 62 (1985) no. 1, pp. 30-44. http://geodesic.mathdoc.fr/item/TMF_1985_62_1_a1/
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     title = {Field algebras in quantum theory with indefinite metric. {II.~Formulation} of a~modular theory in {Pontryagin} space},
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Voir la notice de l'article provenant de la source Math-Net.Ru

The formalism of modular theory for $J$-symmetric weakly closed algebras in Pontryagin space is introduced. Some propositions about the properties of the generalized $J$-Hilbert algebras $\mathscr U$ and $\mathscr U'$ are proved. The main tool in the proofs is the definitizing operator method.

[1] Dadashyan K. Yu., Khoruzhii S. S., TMF, 54:1 (1983), 57–77 | MR | Zbl

[2] Takesaki M., Tomita's theory of modular Hilbert algebras and its applications, Springer-Verlag, B.–N.-Y.–H., 1970 | MR

[3] Bognar J., Indefinite inner product spaces, Springer-Verlag, B.–N.-Y.–H., 1974 | MR | Zbl

[4] Jonas P., Beiträge zur Analysis, 16 (1981), 121–135 | MR | Zbl

[5] Funktsionalnyi analiz, Spravochnaya matematicheskaya biblioteka, Nauka, M., 1972 | MR

[6] Krein M. G., Langer G. K., DAN SSSR, 152:1 (1963), 39–42 | MR | Zbl

[7] Strocchi F., Wightman A. S., J. Math. Phys., 15:10 (1974), 2198–2225 | DOI | MR

[8] Van Daele A., J. Funct. Anal., 15:4 (1974), 378–392 | DOI | MR

[9] Bratteli U., Robinson D., Operatornye algebry i kvantovaya statisticheskaya mekhanika, t. I, Mir, M., 1982 | MR | Zbl

[10] Shulman V. S., Matem. sb., 89:2 (1972), 264–279

[11] Rieffel M., Van Daele A., Pacific J. Math., 69:1 (1977), 187–221 | DOI | MR