A classification of type I AW*-algebras and Boolean valued analysis

Masanao OZAWA

doi:10.2969/jmsj/03640589

A classification of type I AW^*-algebras and Boolean valued analysis

Masanao OZAWA

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JOURNAL FREE ACCESS

1984 Volume 36 Issue 4 Pages 589-608

DOI https://doi.org/10.2969/jmsj/03640589

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Published: 1984 Received: August 30, 1983 Available on J-STAGE: October 20, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) N. Aronszajn, Theory of reproducing kernels, Trans. Amer. Math. Soc., 68 (1950), 337-404.
2) S. K. Berberian, Baer *-rings, Springer, Berlin, 1972.
3) P. R. Halmos, Lectures on Boolean algebras, van Nostrand, New York, 1963.
4) T. Jech, Set theory, Academic Press, New York, 1978.
5) I. Kaplansky, Projections in Banach algebras, Ann. of Math., 53 (1951), 235-249.
6) I. Kaplansky, Algebras of type I, Ann. of Math., 56 (1952), 460-472.
7) I. Kaplansky, Modules over operator algebras, Amer. J. Math., 75 (1953), 839-858.
8) M. Ozawa, Boolean valued interpretation of Hilbert space theory, J. Math. Soc. Japan, 35 (1983), 609-627.
9) W. L. Paschke, Inner product modules over B^*-algebras, Trans. Amer. Math. Soc.,182 (1973), 443-468.
10) M. A. Rieffel, Morita equivalence for C^*-algebras and W^*-algebras, J. Pure Appl. Alg., 5 (1974), 51-96.
11) M. Takesaki, Theory of operator algebras I, Springer, New York, 1979.
12) G. Takeuti, Two applications of logic to mathematics, Iwanami and Princeton University Press, Tokyo and Princeton, 1978.
13) G. Takeuti, A transfer principle in harmonic analysis, J. Symbolic Logic, 44 (1979), 417-440.
14) G. Takeuti, Von Neumann algebras and Boolean valued analysis, J. Math. Soc. Japan, 35 (1983), 1-21.
15) G. Takeuti, C^*-algebras and Boolean valued analysis, Japan. J. Math., 9 (1983), 207-246.
16) G. Takeuti and W. M. Zaring, Axiomatic set theory, Springer, Heidelberg, 1973.

Right : [1] N. Aronszajn, Theory of reproducing kernels, Trans. Amer. Math. Soc., 68 (1950), 337-404.
[2] S. K. Berberian, Baer *-rings, Springer, Berlin, 1972.
[3] P. R. Halmos, Lectures on Boolean algebras, van Nostrand, New York, 1963.
[4] T. Jech, Set theory, Academic Press, New York, 1978.
[5] I. Kaplansky, Projections in Banach algebras, Ann. of Math., 53 (1951), 235-249.
[6] I. Kaplansky, Algebras of type I, Ann. of Math., 56 (1952), 460-472.
[7] I. Kaplansky, Modules over operator algebras, Amer. J. Math., 75 (1953), 839-858.
[8] M. Ozawa, Boolean valued interpretation of Hilbert space theory, J. Math. Soc. Japan, 35 (1983), 609-627.
[9] W. L. Paschke, Inner product modules over B-algebras, Trans. Amer. Math. Soc.,182 (1973), 443-468.
[10] M. A. Rieffel, Morita equivalence for C-algebras and W-algebras, J. Pure Appl. Alg., 5 (1974), 51-96.
[11] M. Takesaki, Theory of operator algebras I, Springer, New York, 1979.
[12] G. Takeuti, Two applications of logic to mathematics, Iwanami and Princeton University Press, Tokyo and Princeton, 1978.
[13] G. Takeuti, A transfer principle in harmonic analysis, J. Symbolic Logic, 44 (1979), 417-440.
[14] G. Takeuti, Von Neumann algebras and Boolean valued analysis, J. Math. Soc. Japan, 35 (1983), 1-21.
[15] G. Takeuti, C-algebras and Boolean valued analysis, Japan. J. Math., 9 (1983), 207-246.
[16] G. Takeuti and W. M. Zaring, Axiomatic set theory, Springer, Heidelberg, 1973.

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