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A classification of factors. (English) Zbl 0206.12901


MSC:

46M05 Tensor products in functional analysis
46L10 General theory of von Neumann algebras
46-02 Research exposition (monographs, survey articles) pertaining to functional analysis
46L35 Classifications of \(C^*\)-algebras
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[1] Araki, H., A lattice of von Neumann algebras associated with the quantum theory of a free Bose field, J. Math. Phys. 4 (1963), 1343-1362. · Zbl 0132.43805 · doi:10.1063/1.1703912
[2] Araki, H. and E. J. Woods, Complete Boolean algebras of type I factors, Publ. RIMS, Kyoto Univ. Ser. A, 2 (1966), 157-242. · Zbl 0169.17601 · doi:10.2977/prims/1195195888
[3] Araki, H., Type of von Neumann algebra associated with free field, Progr. Theoret. Phys. 32 (1964), 956-965. · Zbl 0132.43901 · doi:10.1143/PTP.32.956
[4] Araki, H. and E. J. Woods, Representations of the canonical commutation relations describing a nonrelativistic infinite free Bose gas, J. Math. Phys. 4 (1963), 637-662.
[5] Araki, H. and W. Wyss. Representations of canonical anticommutation relations, Helv. Phys. Acta, 37 (1964), 136-159. · Zbl 0137.23903
[6] Bures, D., Certain factors constructed as infinite tensor products, Comp. Math. 15 (1963), 169-191. · Zbl 0144.37803
[7] dell’ Antonio, G. F., Structure of the algebras of some free systems, Preprint. · Zbl 0159.29002 · doi:10.1007/BF01645837
[8] Dixmier, J., Les algebres d’operateurs dans 1’espace hilbertien, Gauthier-Villars, Paris, 1957.
[9] Loeve, M., Probability theory, Van Nostrand, New York, 1957. · Zbl 0359.60001
[10] Moore, C. C., Invariant measures on product spaces. Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability, vol. II, part 2 (447-459), University of California, Berkeley, 1967. (1936), 116-229.
[11] von Neumann, J., On infinite direct products. Comp. Math. 6 (1938), 1-77. · Zbl 0019.31103
[12] Powers, R. T., Representations of uniformly hyperfinite algebras and their associated von Neumann rings, Ann. of Math. 86 (1967), 138-171. · Zbl 0157.20605 · doi:10.2307/1970364
[13] Pukanszky, L., Some examples of factors, Publ. Math. Debrecen, 4 (1955-56), 135-156.
[14] Rideau, G., On some representations of the anticommutation relations, Preprint. · Zbl 0149.23601 · doi:10.1007/BF02827732
[15] Sakai, S., On topological properties of FT*-algebras, Proc. Japan Acad. 33 (1957), 439-444. · Zbl 0081.11103 · doi:10.3792/pja/1195524953
[16] Schwartz, J., Two finite, non-hyperfinite, non-isomorphic factors, Comm. Pure Appl. Math. 16 (1963), 19-26. · Zbl 0131.33201 · doi:10.1002/cpa.3160160104
[17] Shale, D. and W. F. Stinespring, States of the Clifford algebra, Ann. of Math. 80 (1964), 365-381. · Zbl 0178.49301 · doi:10.2307/1970397
[18] Tomita, M., Quasistandard von Neumann algebras, Preprint.
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