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Embedding as a double commutator in a type I $ AW\sp{\ast} $-algebra


Author: Herbert Halpern
Journal: Trans. Amer. Math. Soc. 148 (1970), 85-98
MSC: Primary 46.65
DOI: https://doi.org/10.1090/S0002-9947-1970-0256180-X
MathSciNet review: 0256180
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  • [1] J. Dixmier, Les algèbres d'opérateurs dans l'espace hilbertien, Gauthier-Villars, Paris, 1957. MR 20 #1234. MR 0094722 (20:1234)
  • [2] -, Les $ {C^ \ast }$-algèbres et leurs représentations, Gauthier-Villars, Paris, 1964. MR 30 #1404. MR 0171173 (30:1404)
  • [3] M. Goldman, Structure of $ A{W^ \ast }$-algebras. I, Duke Math. J. 23 (1956), 23-34. MR 17, 512; MR 17, 1437. MR 0073949 (17:512f)
  • [4] H. Halpern, A spectral decomposition for self-adjoint elements in the maximum GCR ideal of a von Neumann algebra with applications to noncommutative integration theory, Trans. Amer. Math. Soc. 133 (1968), 281-306. MR 37 #5704. MR 0230139 (37:5704)
  • [5] -, Module homomorphisms of a von Neumann algebra into its center (Trans. Amer. Math. Soc. 140 (1969), 183-193. MR 0241986 (39:3321)
  • [6] R. Kadison, Isometries of operator algebras, Ann. of Math. (2) 54 (1951), 325-338. MR 13, 256. MR 0043392 (13:256a)
  • [7] I. Kaplansky, A theorem of rings of operators, Pacific J. Math. 1 (1951), 227-232. MR 14, 291. MR 0050181 (14:291a)
  • [8] -, Projections in Banach algebras, Ann. of Math. (2) 53 (1951), 235-249. MR 13, 48. MR 0042067 (13:48b)
  • [9] -, Algebras of type I, Ann. of Math. (2) 56 (1952), 460-472. MR 14, 291. MR 0050182 (14:291b)
  • [10] -, Modules over operator algebras, Amer. J. Math. 75 (1953), 839-858. MR 15, 327. MR 0058137 (15:327f)
  • [11] M. Nakai, Some expectations in $ A{W^\ast}$-algebras, Proc. Japan Acad. 34 (1958), 411-416. MR 20 #1924. MR 0095422 (20:1924)
  • [12] S. Sakai, A characterization of $ {W^\ast}$-algebras, Pacific J. Math. 6 (1956), 763-773. MR 18, 811. MR 0084115 (18:811f)
  • [13] -, On linear functionals of $ {W^\ast}$-algebras, Proc. Japan Acad. 34 (1958), 571-574. MR 21 #5915. MR 0107190 (21:5915)
  • [14] M. Takesaki, On the conjugate space of operator algebra, Tôhoku Math. J. (2) 10 (1958), 194-203. MR 20 #7227. MR 0100799 (20:7227)
  • [15] -, On the Hahn-Banach type theorem and the Jordan decomposition of module linear mapping over some operator algebras, Kōdai Math. Sem. Rep. 12 (1960), 1-10. MR 22 # 5914. MR 0115112 (22:5914)
  • [16] J. Tomiyama, On the projection of norm one in $ {W^\ast}$-algebras, Proc. Japan Acad. 33 (1957), 608-612. MR 20 #2635. MR 0096140 (20:2635)
  • [17] G. Vincent-Smith, The Hahn-Banach theorem for modules, Proc. London Math. Soc. (3) 17 (1967), 72-90. MR 35 #766. MR 0209870 (35:766)
  • [18] H. Widom, Embedding in algebras of type I, Duke Math. J. 23 (1956), 309-324. MR 17, 1228. MR 0078668 (17:1228c)
  • [19] T. Yen, Trace on finite $ A{W^\ast}$-algebras, Duke Math. J. 22 (1955), 207-222. MR 16, 1033. MR 0069404 (16:1033c)

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DOI: https://doi.org/10.1090/S0002-9947-1970-0256180-X
Article copyright: © Copyright 1970 American Mathematical Society

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