Duality and von Neumann algebras
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- by Masamichi Takesaki PDF
- Bull. Amer. Math. Soc. 77 (1971), 553-557
References
- François Combes, Poids sur une $C^{\ast }$-algèbre, J. Math. Pures Appl. (9) 47 (1968), 57–100 (French). MR 236721
- F. Combes, Poids associé à une algèbre hilbertienne à gauche, Compositio Math. 23 (1971), 49–77 (French). MR 288590
- Jacques Dixmier, Les $C^{\ast }$-algèbres et leurs représentations, Cahiers Scientifiques, Fasc. XXIX, Gauthier-Villars Éditeur, Paris, 1969 (French). Deuxième édition. MR 0246136
- John Ernest, Hopf-von Neumann algebras, Functional Analysis (Proc. Conf., Irvine, Calif., 1966) Academic Press, London; Thompson Book Co., Washington, D.C., 1967, pp. 195–215. MR 0223909
- Pierre Eymard, L’algèbre de Fourier d’un groupe localement compact, Bull. Soc. Math. France 92 (1964), 181–236 (French). MR 228628, DOI 10.24033/bsmf.1607
- K. H. Hofmann, The duality of compact semigroups and $C^*$-bigebras, Lecture Notes in Mathematics, Vol. 129, Springer-Verlag, Berlin-New York, 1970. MR 0432803, DOI 10.1007/BFb0071210
- G. I. Kac, Ring groups and the duality principle, Trudy Moskov. Mat. Obšč. 12 (1963), 259–301 (Russian). MR 0156921
- Kazuyuki Saitô, On a duality for locally compact groups, Tohoku Math. J. (2) 20 (1968), 355–367. MR 238997, DOI 10.2748/tmj/1178243142
- I. E. Segal, A non-commutative extension of abstract integration, Ann. of Math. (2) 57 (1953), 401–457. MR 54864, DOI 10.2307/1969729
- W. Forrest Stinespring, Integration theorems for gages and duality for unimodular groups, Trans. Amer. Math. Soc. 90 (1959), 15–56. MR 102761, DOI 10.1090/S0002-9947-1959-0102761-9
- Masamichi Takesaki, A characterization of group algebras as a converse of Tannaka-Stinespring-Tatsuuma duality theorem, Amer. J. Math. 91 (1969), 529–564. MR 244437, DOI 10.2307/2373525
- M. Takesaki, Tomita’s theory of modular Hilbert algebras and its applications, Lecture Notes in Mathematics, Vol. 128, Springer-Verlag, Berlin-New York, 1970. MR 0270168, DOI 10.1007/BFb0065832 13. M. Takesaki, The theory of operator algebras, Lecture Notes UCLA, Los Angeles, Calif., 1969/70. 14. T. Tannaka, Über den Dualität der nichtkommutativen topologischen Gruppen, Tôhoku Math. J. 45 (1938), 1-12.
- Nobuhiko Tatsuuma, A duality theorem for locally compact groups, J. Math. Kyoto Univ. 6 (1967), 187–293. MR 217222, DOI 10.1215/kjm/1250524377
- Minoru Tomita, On canonical forms of von Neumann algebras, Fifth Functional Analysis Sympos. (Tôhoku Univ., Sendai, 1967) Tôhoku Univ., Math. Inst., Sendai, 1967, pp. 101–102 (Japanese). MR 0284822
- Martin E. Walter, Group duality and isomorphisms of Fourier and Fourier-Stieltjes algebras from a $W^{\ast }$-algebra point of view, Bull. Amer. Math. Soc. 76 (1970), 1321–1325. MR 284823, DOI 10.1090/S0002-9904-1970-12659-3
Additional Information
- Journal: Bull. Amer. Math. Soc. 77 (1971), 553-557
- MSC (1970): Primary 46L10, 22D35, 22D25
- DOI: https://doi.org/10.1090/S0002-9904-1971-12752-0
- MathSciNet review: 0305095