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Duality and von Neumann algebras

Part of the Lecture Notes in Mathematics book series (LNM,volume 247)

Keywords

  • Hilbert Space
  • Compact Group
  • Banach Algebra
  • Duality Theorem
  • Regular Representation

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References

  1. N. Bourbaki, Integration, Chap. VII and VIII, Paris, 1967.

    Google Scholar 

  2. H. Cartan and R. Godement, Théorie de la dualité et analyse harmonique, Ann. Scient. Éc. Norm. Sup., 64 (1947), 77–99.

    MathSciNet  MATH  Google Scholar 

  3. F. Combes, Poids sur une C*-algèbre, J. Math. pure et appl., 47 (1968), 57–100.

    MathSciNet  MATH  Google Scholar 

  4. _____, Poids associé à une algèbre hilbertienne a gauche, to appear.

    Google Scholar 

  5. J. Dixmier, Formes linéaires sur un anneau d'opérateurs, Bull. Soc. Math. France, 87 (1953), 9–39.

    MathSciNet  MATH  Google Scholar 

  6. _____, Les algebres d'operateurs dans l'espace hilbertien, Gaushier-Villars, 2nd edition, 1969.

    Google Scholar 

  7. _____, Les C*-algebres et leurs represéntations, Gaushier-Villars, 1965.

    Google Scholar 

  8. J. Ernest, Hopf-von Neumann algebras, Lecture in Functional Analysis Conference at Irvine, 1966.

    Google Scholar 

  9. _____, A strong duality for separable locally compact groups, to appear.

    Google Scholar 

  10. P. Eymard, L'algèbre de Fourier d'un groupe localement compact, Bull. Soc. Math., France, 92 (1964), 181–236.

    MathSciNet  MATH  Google Scholar 

  11. G. Hochschild, The structure of Lie groups, Holden-Day, 1965.

    Google Scholar 

  12. K. H. Hofmann, The duality of compact semigroups, and C*-bigebras, Springer-Verlag, Lecture Notes Ser., 129 (1970).

    Google Scholar 

  13. G. I. Kac, Ring-groups and the principle of duality. I, II, Trudy Moskov Mat. Obsc., 12 (1963), 259–301; 13 (1965), 84–113.

    MathSciNet  Google Scholar 

  14. J. L. Kelley, Duality for compact groups, Proc. Nat. Acad. Sci., 49 (1963), 457–458.

    CrossRef  MathSciNet  MATH  Google Scholar 

  15. M. Krein, A duality principle for bicompact groups and quadratic block algebras, Doklady Akad. Nauk SSSR, 69 (1949), 725–728.

    MathSciNet  Google Scholar 

  16. L. H. Loomis, An introduction to abstract harmonic analysis, Van Nostrand, 1953.

    Google Scholar 

  17. Y. Misonou, On the direct product of W*-algebras, Tohoku Math. J., 6 (1954), 189–204.

    CrossRef  MathSciNet  MATH  Google Scholar 

  18. W. Rudin, Fourier analysis on groups, Interscience Publishers, 1962.

    Google Scholar 

  19. K. Saito, On a duality for locally compact groups, Tohoku Math. J., 20 (1968), 355–367.

    CrossRef  MathSciNet  MATH  Google Scholar 

  20. S. Sakai, The theory of W*-algebras, Lecture Notes, Yale Univ., 1962.

    Google Scholar 

  21. I. E. Segal, An extension of Plancherel's formula to separable unimodular locally compact groups, Ann. Math., 52 (1950), 272–292.

    CrossRef  MATH  Google Scholar 

  22. _____, A non-commutative extension of abstract integration, Ann. Math., 57 (1953), 401–457.

    CrossRef  MathSciNet  MATH  Google Scholar 

  23. W. F. Stinespring, Integration theorems for gages and duality for unimodular groups, Trans. Amer. Math. Soc., 90 (1959), 15–56.

    CrossRef  MathSciNet  MATH  Google Scholar 

  24. S. Takahashi, A duality theorem for representable locally compact groups with compact commutator subgroup, Tohoku Math. J., 4 (1952), 115–121.

    CrossRef  MathSciNet  MATH  Google Scholar 

  25. _____, A characterization of group rings as special classes of Hopf-algebras, Canad. Math. Bull., 8 (1965), 465–475.

    CrossRef  MathSciNet  MATH  Google Scholar 

  26. M. Takesaki, A characterization of group algebras as a converse of Tannaka-Stinespring-Tatsuuma duality, Amer. J. Math., 91 (1969), 529–564.

    CrossRef  MathSciNet  MATH  Google Scholar 

  27. , A generalized commutation relation for the regular representation, Bull. Soc. Math., France, 97 (1969), 289–297.

    MathSciNet  MATH  Google Scholar 

  28. ____, Tomita's theory for modular Hilbert algebras and its applications, Springer-Verlag Lecture Notes Ser., 128 (1970).

    Google Scholar 

  29. ____, The theory of operator algebras, Lecture Notes, UCLA, 1969/70.

    Google Scholar 

  30. M. Takesaki and N. Tatsuuma, Duality and subgroups, to appear in Ann. Math.

    Google Scholar 

  31. T. Tannaka, Über den Dualität der nichtkommutativen topologischen Gruppen, Tôhoku Math. J., 45 (1938), 1–12.

    MATH  Google Scholar 

  32. N. Tatsuuma, A duality theorem for locally compact groups I, Proc. Japan Acad., 41 (1965), 878–882.

    CrossRef  MathSciNet  MATH  Google Scholar 

  33. ____, A duality theorem for locally compact groups II, Proc. Japan Acad., 42 (1966), 46–47.

    CrossRef  MathSciNet  Google Scholar 

  34. ____, A duality theorem for locally compact groups, J. Math. Kyoto Univ., 6 (1967), 187–293.

    MathSciNet  MATH  Google Scholar 

  35. M. Tomita, Standard forms of von Neumann algebras, The Vth Functional Analysis Symposium of the Math. Soc. of Japan, Sendai, 1967.

    Google Scholar 

  36. T. Turumaru, On the direct product of operator algebras, III, Tôhoku Math. J., 6 (1954), 208–211.

    CrossRef  MathSciNet  MATH  Google Scholar 

  37. M. E. Walter, Group duality and isomorphisms of Fourier and Fourier-Stieltjes algebras from a W*-algebra point of view, to appear in Bull. Amer. Math. Soc.

    Google Scholar 

  38. A. Weil, L'intégration dans les groupes topologiques et ses applications, Paris, 1940.

    Google Scholar 

  39. J. G. Wendel, Left centralizers and isomorphisms of group algebras, Pacific J. Math., 2 (1952), 251–261.

    CrossRef  MathSciNet  MATH  Google Scholar 

References

  1. J. Dixmier, Les algèbres d'opératuers dans l'espace hilbertien, Gauthier-Villar, Paris, 2nd edition (1969).

    MATH  Google Scholar 

  2. N. Dunford and J. T. Schwartz, Linear operators II, New York (1963).

    Google Scholar 

  3. S. Sakai, On the tensor product of W*-algebras, Amer. J. Math., 90 (1968), 335–341.

    CrossRef  MathSciNet  MATH  Google Scholar 

  4. M. Takesaki, Tomita's theory of modular Hilbert algebras and its applications, Springer-Verlag, Lecture Notes, no. 128 (1970).

    Google Scholar 

  5. M. Tomita, Standard forms of von Neumann algebras, the Vth Functional Analysis Symposium of the Math. Soc. of Japan, Sendai (1967).

    Google Scholar 

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© 1972 Springer-Verlag

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Takesaki, M. (1972). Duality and von Neumann algebras. In: Lectures on Operator Algebras. Lecture Notes in Mathematics, vol 247. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0058558

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  • DOI: https://doi.org/10.1007/BFb0058558

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