Geodesic
Field algebras in quantum theory with indefinite metric.~IV
Teoretičeskaâ i matematičeskaâ fizika, Tome 72 (1987) no. 3, pp. 340-351

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Construction of basic elements of modular theory for $WJ^*$-algebras (weakly closed unital $J$-involutive operator algebras) in Pontryagin spaces is completed. Tomita's fundamental theorem is proved without the restrictions imposed in the part III. It is found that for a $WJ^*$-algebra satisfying the bicommutant theorem separating vectors are cyclic for its commutant. KMS boundary condition and the uniqueness of the modular group implementing this condition are proved. 
@article{TMF_1987_72_3_a1,
     author = {K. Yu. Dadashyan and S. S. Horuzhy},
     title = {Field algebras in quantum theory with indefinite {metric.~IV}},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {340--351},
     publisher = {mathdoc},
     volume = {72},
     number = {3},
     year = {1987},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1987_72_3_a1/}
}
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K. Yu. Dadashyan; S. S. Horuzhy. Field algebras in quantum theory with indefinite metric.~IV. Teoretičeskaâ i matematičeskaâ fizika, Tome 72 (1987) no. 3, pp. 340-351. http://geodesic.mathdoc.fr/item/TMF_1987_72_3_a1/