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Teoreticheskaya i Matematicheskaya Fizika, 1987, Volume 70, Number 2, Pages 181–191
(Mi tmf4609)
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This article is cited in 4 scientific papers (total in 4 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.
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
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https://www.mathnet.ru/eng/tmf4609 https://www.mathnet.ru/eng/tmf/v70/i2/p181
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Abstract page: | 405 | Full-text PDF : | 111 | References: | 62 | First page: | 1 |
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