[1] |
Araki, H., A classifiction of factors, II.Publications of Research Institute for Math. Sciences, Kyoto University, Ser. A, 4 (1968), 585–593. · Zbl 0198.17803 · doi:10.2977/prims/1195194819 |
[2] |
Araki, H.,Structure of some von Neumann algebras with isolated discrete modular spectrum. To appear. · Zbl 0269.46048 |
[3] |
Araki, H. &Woods, J., A classification of factors.Publications of Research Institute for Math. Sciences, Kyoto University, Ser. A, 4 (1968), 51–130. · Zbl 0206.12901 · doi:10.2977/prims/1195195263 |
[4] |
Arveson, W.,On groups of automorphisms of operator algebras. To appear. · Zbl 0296.46064 |
[5] |
Blattner, R. J., On induced representations.Amer. J. Math., 83 (1961), 79–98. · Zbl 0122.28405 · doi:10.2307/2372722 |
[6] |
–, On a theorem of G. W. Mackey.Bull. Amer. Math. Soc., 68 (1962), 585–587. · Zbl 0122.35202 · doi:10.1090/S0002-9904-1962-10859-3 |
[7] |
Bourbaki, N.,Intégration, Chap. 1–4, Paris (1952). · Zbl 0049.31703 |
[8] |
Bourbaki, N.,Intégration, Chap. 7–8, Paris (1963). · Zbl 0156.03204 |
[9] |
Combes, F., Poids associés à une algèbre hilbertienne à gauche.Comp. Math., 23 (1971), 49–77. · Zbl 0208.38201 |
[10] |
Connes, A.,Une classification des facteurs de type III. Thesis, to appear. · Zbl 0243.46064 |
[11] |
Dixmier, J.,Les algèbres d’opérateurs dans l’espace hilbertien, 2nd edition, Paris, Gauthier-Villars, (1969). · Zbl 0175.43801 |
[12] |
Dotlicher, S., Kaspler, D. &Robinson, D., Covariance algebras in field theory and statistical mechanics.Comm. Math. Phys., 3 (1966), 1–28. · Zbl 0152.23803 · doi:10.1007/BF01645459 |
[13] |
Haga, Y.,On subalgebras of a crossed product von Neumann algebra. To appear. · Zbl 0268.46059 |
[14] |
Haga, Y. & Takeda, Z., Correspondence between subgroups and subalgebras in a cross product von Neumann algebra. To appear inTôhoku Math. J. · Zbl 0246.46052 |
[15] |
Herman, R. &Takesaki, M., States and automorphism groups of operator algebras.Comm. Math. Phys., 19 (1940), 142–160. · Zbl 0206.13001 · doi:10.1007/BF01646631 |
[16] |
Ionescu Tulcea, A. andIonescu Tulcea, C.,Topics in the theory of lifting. Springer-Verlag, New York, (1969). · Zbl 0179.46303 |
[17] |
Ionescu Tulcea, A. andIonescu Tulcea, C.,On the existence of a lifting commuting with the left translations of an arbitrary locally compact groups, Proc. Fifth Berkeley Symp. in Math. Stat. and Prob. Univ. of California Press, (1967), 63–97. · Zbl 0201.49202 |
[18] |
Loomis, L. H., Note on a theorem of Mackay.Duke Math. J., 19 (1952), 641–645. · Zbl 0047.35501 · doi:10.1215/S0012-7094-52-01968-6 |
[19] |
Mackey, G. W., A theorem of Stone and von Neumann.Duke Math. J., 16 (1949), 313–326. · Zbl 0036.07703 · doi:10.1215/S0012-7094-49-01631-2 |
[20] |
–, Induced representations of locally compact groups, I.Ann. Math., 55 (1952), 101–139. · Zbl 0046.11601 · doi:10.2307/1969423 |
[21] |
–, Unitary representations of group extensions.Acta Math., 99 (1958), 265–311. · Zbl 0082.11301 · doi:10.1007/BF02392428 |
[22] |
Maréchal, O., Champs measureables d’espaces hilbertiens.Bull. Sc. Math., 93 (1969), 113–143. · Zbl 0186.45601 |
[23] |
McDuff, D., A countable infinity of II1 factors.Ann. Math., 90 (1969), 361–371. · Zbl 0184.16901 · doi:10.2307/1970729 |
[24] |
–, Uncountably many II1 factors.Ann. Math., 90 (1969), 372–377. · Zbl 0184.16902 · doi:10.2307/1970730 |
[25] |
Murray, F. J. &von Neumann, J., On rings of operators.Ann. Math., 37 (1936), 116–229. · Zbl 0014.16101 · doi:10.2307/1968693 |
[26] |
–, On rings of operators IV.Ann. Math., 44 (1943), 716–808. · Zbl 0060.26903 · doi:10.2307/1969107 |
[27] |
Nakamura, M. &Takeda, Z., On some elementary properties of the crossed products of von Neumann algebras.Proc. Japan Acad., 34 (1958), 489–494. · Zbl 0085.09905 · doi:10.3792/pja/1195524559 |
[28] |
–, A Galois theory for finite factors.Proc. Japan Acad., 36 (1960), 258–260. · Zbl 0098.30804 · doi:10.3792/pja/1195524026 |
[29] |
–, On the fundamental theorem of the Galois theory for finite factors.Proc. Japan Acad., 36 (1960), 313–318. · Zbl 0094.09803 · doi:10.3792/pja/1195523999 |
[30] |
Nakamura, M. &Umegaki, H., Heisenberg’s commutation relation and the Plancherel theorem.Proc. Japan Acad., 37 (1961), 239–242. · Zbl 0101.09404 · doi:10.3792/pja/1195523709 |
[31] |
von Neumann, J., Die Eindeutigkeit der Schrödingerschen Operatoren.Math. Ann., 104 (1931), 570–578. · Zbl 0001.24703 · doi:10.1007/BF01457956 |
[32] |
Nielsen, O. A.,The Mackey-Blattner theorem and Takesaki’s generalized commutation relation for locally compact groups. To appear. · Zbl 0256.22010 |
[33] |
Pedersen, G. K. &Takesaki, M., The Radon-Nikodym theorem for von Neumann algebras.Acta Math., 130 (1973), 53–87. · Zbl 0262.46063 · doi:10.1007/BF02392262 |
[34] |
Powers, R., Representations of uniformly hyperfinite algebras and their associated von Neumann rings.Ann. Math., 86 (1967), 138–171. · Zbl 0157.20605 · doi:10.2307/1970364 |
[35] |
Rudin, W.,Fourier analysis on groups. Intersciences, New York, (1962). · Zbl 0107.09603 |
[36] |
Sakai, S., An uncountable number of II1 and IIfactors.J. Functional Analysis, 5 (1970), 236–246. · Zbl 0198.17804 · doi:10.1016/0022-1236(70)90028-5 |
[37] |
Størmer, E.,Spectra of states, and asymptotically abelian C *-algebras. To appear. · Zbl 0245.46085 |
[38] |
Suzuki, N., Cross products of rings of operators.Tôhoku Math. J., 11 (1959), 113–124. · Zbl 0106.31005 · doi:10.2748/tmj/1178244632 |
[39] |
Takesaki, M., Covariant representations ofC *-algebras and their locally compact automorphism groups.Acta Math., 119 (1967), 273–303. · Zbl 0163.36802 · doi:10.1007/BF02392085 |
[40] |
–, A liminal crossed product of a uniformly hyperfiniteC *-algebra by a compact abelian automorphism group.J. Functional Analysis, 7 (1971), 140–146. · Zbl 0229.46055 · doi:10.1016/0022-1236(71)90049-8 |
[41] |
–, A generalized commutation relation for the regular representation.Bull. Soc. Math., France, 97 (1969), 289–297. · Zbl 0188.20101 |
[42] |
Takesaki, M.,Tomita’s theory of modular Hilbert algebras and its application. Lecture Notes in Mathematics, 128, Springer-Verlag, (1970). · Zbl 0193.42502 |
[43] |
Takesaki, M.,States and automorphisms of operator algebras–Standard representations and the Kubo-Martin-Schwinger boundary condition. Summer Rencontres in Mathematics and Physics, Battelle Seattle, (1971). · Zbl 0258.46055 |
[44] |
Takesaki, M., Periodic and homogeneous states on a von Neumann algebras, I, II, III. To appear inBull. Amer. Math. Soc. |
[45] |
–, The structure of a von Neumann algebra with a homogeneous periodic state.Acta Math., 131 (1973), 79–121. · Zbl 0267.46047 · doi:10.1007/BF02392037 |
[46] |
–, Dualité dans les produits croisés d’algebres de von Neumann.C. R. Acad. Sc. Paris, Ser. A, 276 (1973), 41–43. |
[47] |
Takesaki, M., Algèbres de von Neumann proprement infinits et produits croisés.C. R. Acad. Sc. Paris, Ser. A, 276 (1973). · Zbl 0247.46068 |
[48] |
Takesaki, M., Duality in crossed products and von Neumann algebras of type III. To appearBull. Amer. Math. Soc. · Zbl 0269.46047 |
[49] |
Takesaki, M. &Tatsuuma, N., Duality and subgroups.Ann. Math., 93 (1971), 344–364. · doi:10.2307/1970778 |
[50] |
Tomita, M., Standard forms of von Neumann algebras.The 5th Functional Analysis Symposium of the Math. Soc. of Japan, Sendai, (1967). |
[51] |
Turumaru, T., Crossed product of operator algebras.Tôhoka Math. J., 10 (1958), 355–365. · Zbl 0087.31803 · doi:10.2748/tmj/1178244669 |
[52] |
Vesterstrøm, J. &Wils, W., Direct integrals of Hilbert spaces, II.Math. Scand., 26 (1970), 89–102. · Zbl 0207.44005 |
[53] |
Zeller-Meier, G., Produits croisés d’uneC *-algebre par un groupe d’automorphismes.J. Math. Pures et appl., 47 (1968), 101–239. · Zbl 0165.48403 |
[54] |
A. Connes & Van Daele, The group property of the invariant S. To appear inMath. Scand. · Zbl 0268.46056 |