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TMF, 1987, Volume 70, Number 2, Pages 181–191 (Mi tmf4609)  

This article is cited in 2 scientific papers (total in 2 papers)

Field algebras in quantum theory with indefinite metric. III. Spectrum of modular operator and Tomita's fundamental theorem

K. Yu. Dadashyan, S. S. Horuzhy


Abstract: Formulation of modular theory for weakly closed $J$-involutive algebras of bounded operators in Pontryagin spaces is continued. Spectrum of the modular operator of such an algebra is investigated in detail. The existence of strongly continuous $J$-unitary group $\Delta^{it}$, $t\in \mathbb{R}$, is established and Tomita's fundamental theorem is proved under the assumption that the spectrum of $\Delta$ belongs to the right half-plane.

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English version:
Theoretical and Mathematical Physics, 1987, 70:2, 125–133

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Received: 23.12.1985

Citation: K. Yu. Dadashyan, S. S. Horuzhy, “Field algebras in quantum theory with indefinite metric. III. Spectrum of modular operator and Tomita's fundamental theorem”, TMF, 70:2 (1987), 181–191; Theoret. and Math. Phys., 70:2 (1987), 125–133

Citation in format AMSBIB
\Bibitem{DadHor87}
\by K.~Yu.~Dadashyan, S.~S.~Horuzhy
\paper Field algebras in quantum theory with indefinite metric.~III. Spectrum of modular operator and Tomita's fundamental theorem
\jour TMF
\yr 1987
\vol 70
\issue 2
\pages 181--191
\mathnet{http://mi.mathnet.ru/tmf4609}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=894465}
\zmath{https://zbmath.org/?q=an:0642.46063}
\transl
\jour Theoret. and Math. Phys.
\yr 1987
\vol 70
\issue 2
\pages 125--133
\crossref{https://doi.org/10.1007/BF01039201}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1987K225600003}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. K. Yu. Dadashyan, S. S. Horuzhy, “Field algebras in quantum theory with indefinite metric. IV”, Theoret. and Math. Phys., 72:3 (1987), 921–929  mathnet  crossref  mathscinet  zmath
    2. S. N. Litvinov, “Bicyclic $WJ*$-algebras in Pontryagin space of type $\Pi_1$”, Funct. Anal. Appl., 26:3 (1992), 188–195  mathnet  crossref  mathscinet  zmath  isi
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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