Irreducible module homomorphisms of a von Neumann algebra into its center

Halpern, Herbert

doi:10.1090/S0002-9947-1969-0241987-7

Irreducible module homomorphisms of a von Neumann algebra into its center
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by Herbert Halpern

Trans. Amer. Math. Soc. 140 (1969), 195-221

DOI: https://doi.org/10.1090/S0002-9947-1969-0241987-7

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References

Jacques Dixmier, Les algèbres d’opérateurs dans l’espace hilbertien (Algèbres de von Neumann), Cahiers Scientifiques, Fasc. XXV, Gauthier-Villars, Paris, 1957 (French). MR 0094722

Les

algèbres et leur représentations

James Glimm, A Stone-Weierstrass theorem for $C^{\ast }$-algebras, Ann. of Math. (2) 72 (1960), 216–244. MR 116210, DOI 10.2307/1970133
James Glimm, Type I $C^{\ast }$-algebras, Ann. of Math. (2) 73 (1961), 572–612. MR 124756, DOI 10.2307/1970319
R. Godement, Sur la théorie des représentations unitaires, Ann. of Math. (2) 53 (1951), 68–124 (French). MR 38571, DOI 10.2307/1969343
Malcolm Goldman, Structure of $AW^*$-algebras. I, Duke Math. J. 23 (1956), 23–34. MR 73949
Herbert Halpern, The maximal $\textrm {GCR}$ ideal in an $\textrm {AW}^{\ast }$-algebra, Proc. Amer. Math. Soc. 17 (1966), 906–914. MR 198265, DOI 10.1090/S0002-9939-1966-0198265-7
Herbert Halpern, An integral representation of a normal functional on a von Neumann algebra, Trans. Amer. Math. Soc. 125 (1966), 32–46. MR 198266, DOI 10.1090/S0002-9947-1966-0198266-3
Herbert Halpern, A spectral decomposition for self-adjoint elements in the maximum $\textrm {GCR}$ ideal of a von Neumann algebra with applications to noncommutative integration theory, Trans. Amer. Math. Soc. 133 (1968), 281–306. MR 230139, DOI 10.1090/S0002-9947-1968-0230139-1
Herbert Halpern, Commutators in properly infinite von Neumann algebras, Trans. Amer. Math. Soc. 139 (1969), 55–73. MR 251546, DOI 10.1090/S0002-9947-1969-0251546-8

Proper values for the elements of the maximal GCR ideal of a von Neumann algebra

Herbert Halpern, Module homomorphisms of a von Neumann algebra into its center, Trans. Amer. Math. Soc. 140 (1969), 183–193. MR 241986, DOI 10.1090/S0002-9947-1969-0241986-5
Richard V. Kadison, Irreducible operator algebras, Proc. Nat. Acad. Sci. U.S.A. 43 (1957), 273–276. MR 85484, DOI 10.1073/pnas.43.3.273
Irving Kaplansky, The structure of certain operator algebras, Trans. Amer. Math. Soc. 70 (1951), 219–255. MR 42066, DOI 10.1090/S0002-9947-1951-0042066-0
Irving Kaplansky, A theorem on rings of operators, Pacific J. Math. 1 (1951), 227–232. MR 50181, DOI 10.2140/pjm.1951.1.227
Irving Kaplansky, Algebras of type $\textrm {I}$, Ann. of Math. (2) 56 (1952), 460–472. MR 50182, DOI 10.2307/1969654
Irving Kaplansky, Modules over operator algebras, Amer. J. Math. 75 (1953), 839–858. MR 58137, DOI 10.2307/2372552
J. L. Kelley and Isaac Namioka, Linear topological spaces, The University Series in Higher Mathematics, D. Van Nostrand Co., Inc., Princeton, N.J., 1963. With the collaboration of W. F. Donoghue, Jr., Kenneth R. Lucas, B. J. Pettis, Ebbe Thue Poulsen, G. Baley Price, Wendy Robertson, W. R. Scott, Kennan T. Smith. MR 0166578, DOI 10.1007/978-3-662-41914-4
Mitsuru Nakai, Some expectations in $AW^{\ast }$-algebras, Proc. Japan Acad. 34 (1958), 411–416. MR 95422
John von Neumann, On rings of operators. Reduction theory, Ann. of Math. (2) 50 (1949), 401–485. MR 29101, DOI 10.2307/1969463
Charles E. Rickart, General theory of Banach algebras, The University Series in Higher Mathematics, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto-London-New York, 1960. MR 0115101

Theory of

algebras

I. E. Segal, Decompositions of operator algebras. I, Mem. Amer. Math. Soc. 9 (1951), 67. MR 44749
Masamichi Takesaki, On the Hahn-Banach type theorem and the Jordan decomposition of module linear mapping over some operator algebras, K\B{o}dai Math. Sem. Rep. 12 (1960), 1–10. MR 115112
Joseph L. Taylor, The Tomita decomposition of rings of operators, Trans. Amer. Math. Soc. 113 (1964), 30–39. MR 167854, DOI 10.1090/S0002-9947-1964-0167854-0
Minoru Tomita, Representations of operator algebras, Math. J. Okayama Univ. 3 (1954), 147–173. MR 62359
Minoru Tomita, Spectral theory of operator algebras. I, Math. J. Okayama Univ. 9 (1959/60), 63–98. MR 117581
Harold Widom, Embedding in algebras of type I, Duke Math. J. 23 (1956), 309–324. MR 78668

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Irreducible module homomorphisms of a von Neumann algebra into its center
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