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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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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
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\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
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\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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http://mi.mathnet.ru/eng/tmf4609 http://mi.mathnet.ru/eng/tmf/v70/i2/p181
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Cycle of papers
- On field algebras in quantum theory with indefinite metric
K. Yu. Dadashyan, S. S. Horuzhy
TMF, 1983, 54:1, 57–77
- Field algebras in quantum theory with indefinite metric. II. Formulation of a modular theory in Pontryagin space
K. Yu. Dadashyan, S. S. Horuzhy
TMF, 1985, 62:1, 30–44
- Field algebras in quantum theory with indefinite metric. III. Spectrum of modular operator and Tomita's fundamental theorem
K. Yu. Dadashyan, S. S. Horuzhy
TMF, 1987, 70:2, 181–191
This publication is cited in the following articles:
-
K. Yu. Dadashyan, S. S. Horuzhy, “Field algebras in quantum theory with indefinite metric. IV”, Theoret. and Math. Phys., 72:3 (1987), 921–929
 -
S. N. Litvinov, “Bicyclic $WJ*$-algebras in Pontryagin space of type $\Pi_1$”, Funct. Anal. Appl., 26:3 (1992), 188–195
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