Literature Cited
K. Yu. Dadashyan and S. S. Khoruzkii, Teor. Mat. Fiz.,54, 57 (1983).
K. Yu. Dadashyan and S. S. Khoruzhii, Teor. Mat. Fiz.,62, 30 (1985).
M. A. Rieffel and A. Van Daele, Pac. J. Math.,69, 187 (1977).
M. Takesaki, Tomita's Theory of Modular Hilbert Algebras and its Applications, Springer-Verlag, Berlin (1970).
J. Bognar, Indefinite Inner Product Spaces, Springer-Verlag, Berlin (1974).
M. Reed and B. Simon, Methods of Modern Mathematical Physics, Vol. 2, Academic Press, New York (1975). (Russian translation published by Mir, Moscow (1978)).
Functional Analysis [in Russian], Spravochnaya Matematicheskaya Biblioteka (Mathematics Reference Library), Nauka, Moscow (1972).
M. G. Krein, “Introduction to the geometry of indefinite J spaces and the theory of operators on these spaces,” in: Second Summer Mathematics School, Part 1 [in Russian], Naukova Dumka, Kiev (1965), p. 15.
N. Dunford and J. T. Schwartz, Linear Operators, Vol. 1, General Theory, Interscience, New York (1958).
O. Bratteli and D. W. Robinson, Operator Algebras and Quantum Statistical Mechanics, Vol. 1, New York (1979). (Russian translation published by Mir, Moscow (1982)).
Additional information
V. A. Steklov Mathematics Institute, USSR Academy of Sciences. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 70, No. 2, pp. 181–191, February, 1987.
Rights and permissions
About this article
Cite this article
Dadashyan, K.Y., Khoruzhii, S.S. Field algebras in quantum theory with indefinite metric. III. Spectrum of modular operator and Tomita's fundamental theorem. Theor Math Phys 70, 125–133 (1987). https://doi.org/10.1007/BF01039201
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01039201