Literature Cited
G. Takeuti, “Von Neumann algebras and Boolean-valued analysis,” J. Math. Soc. Jpn.,35, No. 1, 1–21 (1983).
G. Takeuti, “C*-algebras and Boolean-valued analysis,” Jpn. J. Math.,9, No. 2, 207–245 (1983).
M. Ozawa, “A classification of type I AW*-algebras and Boolean-valued analysis,” J. Math. Soc. Jpn.,36, No. 4, 589–608 (1984).
M. Ozawa, “A transfer principle from von Neumann algebras to AW*-algebras,” J. London Math. Soc.,32, No. 2, 141–148 (1985).
M. Ozawa, “Boolean-valued analysis approach to the trace problem of AW*-algebras” J. London Math. Soc.,33, No. 2, 347–354 (1986).
I. Kaplansky, “Modules over operator algebras,” Am. J. Math.,75, No. 4, 839–858 (1953).
G. Takeuti and W. M. Zarring, Axiomatic Set Theory, Springer, New York (1973).
A. G. Kusraev Vector Duality and Its Applications [in Russian], Nauka, Novosibirsk (1985).
A. G. Kusraev, Elements of Boolean-Valued Analysis [in Russian], Mathematics Institute, Siberian Branch, Academy of Sciences of the USSR, Novosibirsk (1987).
A. G. Kusraev and S. S. Kutateladze, Nonstandard Methods of Analysis [in Russian], Nauka, Novosibirsk (1980).
E. I. Gordon, “Real numbers in Boolean-valued models of set theory and K-space,” Dokl. Akad. Nauk SSSR,237, No. 4, 773–775 (1977).
A. G. Kusraev, “Banach-Kantorovich spaces,” Sib. Mat. Zh.,26, No. 1, 119–126 (1985).
A. G. Kusreev “To a geometry of Banach spaces with a mixed norm,” Dokl. Akad. Nauk SSSR,300, No. 5, 1049–1052 (1988).
A. G. Kusraev, “Linear operators in lattice normed spaces,” in: Investigations in Geometry “in the large” and Mathematical Analysis [in Russian], Nauka, Novosibirsk (1987), pp. 84–123.
V. A. Lyubetskii and E. I. Gordon, “Boolean extensions of uniform structures,” in: Investigations in Nonclassical Logics and Formal Systems [in Russian], Nauka, Moscow (1983), pp. 82–153.
T. J. Jech, Lectures in Set Theory with Particular Emphasis on the Method of Forcing, Lect. Notes Math.,217 (1971).
N. Dunford and J. T. Schwartz, Linear Operators, Interscience, New York (1958-71).
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Novosibirsk City. Translated from Sibirskii Matematicheskii Zhurnal, Vol. 32, No. 3, pp. 78–88, May–June, 1991.
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Kusraev, A.G. Functional realization of AW*-albegras of type I. Sib Math J 32, 416–424 (1991). https://doi.org/10.1007/BF00970477
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DOI: https://doi.org/10.1007/BF00970477