×

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
PDFBibTeX XMLCite
Full Text: DOI

References:

[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
[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
[3] Araki, H., Type of von Neumann algebra associated with free field, Progr. Theoret. Phys. 32 (1964), 956-965. · Zbl 0132.43901
[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
[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
[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
[15] Sakai, S., On topological properties of FT*-algebras, Proc. Japan Acad. 33 (1957), 439-444. · Zbl 0081.11103
[16] Schwartz, J., Two finite, non-hyperfinite, non-isomorphic factors, Comm. Pure Appl. Math. 16 (1963), 19-26. · Zbl 0131.33201
[17] Shale, D. and W. F. Stinespring, States of the Clifford algebra, Ann. of Math. 80 (1964), 365-381. · Zbl 0178.49301
[18] Tomita, M., Quasistandard von Neumann algebras, Preprint.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.