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Cohomology of operator algebras

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Lectures on Operator Algebras

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

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References (Papers)

  1. C. A. Akemann, The dual space of an operator algebra (Trans. Amer. Math. Soc. 126 (1967), 286–302).

    Article  MathSciNet  MATH  Google Scholar 

  2. M. M. Day, Amenable semi-groups (Illinois J. Math. 1 (1957), 509–544).

    MathSciNet  MATH  Google Scholar 

  3. M. M. Day, Ergodic theorems for Abelian semi-groups (Trans. Amer. Math. Soc. 51 (1942), 399–412).

    MathSciNet  MATH  Google Scholar 

  4. G. Hochschild, On the cohomology groups of an associative algebra (Ann. of Math. 46 (1945), 58–67).

    Article  MathSciNet  MATH  Google Scholar 

  5. G. Hochschild, On the cohomology theory for associative algebras (Ann. of Math. 47 (1946), 568–579).

    Article  MathSciNet  MATH  Google Scholar 

  6. G. Hochschild, Cohomology and representations of associative algebras (Duke Math. J. 14 (1947), 921–948).

    Article  MathSciNet  MATH  Google Scholar 

  7. B. E. Johnson, The Wedderburn decomposition of Banach algebras with finite dimensional radical (Amer. J. Math. 90 (1968), 866–876).

    Article  MathSciNet  MATH  Google Scholar 

  8. B. E. Johnson, Cohomology in Banach algebras (to appear).

    Google Scholar 

  9. B. E. Johnson and J. R. Ringrose, Derivations of operator algebras and discrete group algebras (Bull. London Math. Soc. 1 (1969), 70–74).

    Article  MathSciNet  MATH  Google Scholar 

  10. B. E. Johnson and A. M. Sinclair, Continuity of derivations and a problem of Kaplansky (Amer. J. Math. 90 (1968), 1067–1073).

    Article  MathSciNet  MATH  Google Scholar 

  11. R. V. Kadison, Derivations of operator algebras (Ann. of Math. 83 (1966), 280–293).

    Article  MathSciNet  MATH  Google Scholar 

  12. R. V. Kadison and J. R. Ringrose, Derivations and automorphisms of operator algebras (Commun. Math. Phys. 4 (1967), 32–63).

    Article  MathSciNet  MATH  Google Scholar 

  13. R. V. Kadison, E. C. Lance and J. R. Ringrose, Derivations and automorphisms of operator algebras II (J. Functional Analysis 1 (1967), 204–221).

    Article  MathSciNet  MATH  Google Scholar 

  14. R. V. Kadison and J. R. Ringrose, Cohomology of operator algebras I. Type I von Neumann algebras (Acta Math. 126 (1971)).

    Google Scholar 

  15. R. V. Kadison and J. R. Ringrose, Cohomology of operator algebras II. Extended cobounding and the hyperfinite case (Arkiv för Matematik 9 (1971)).

    Google Scholar 

  16. R. V. Kadison, B. E. Johnson and J. R. Ringrose, Cohomology of operator algebras III. Reduction to normal cohomology (to appear).

    Google Scholar 

  17. I. Kaplansky, Modules over operator algebras (Amer. J. Math. 75 (1953), 839–859).

    Article  MathSciNet  MATH  Google Scholar 

  18. R. T. Powers, Representations of uniformly hyperfinite algebras and their associated von Neumann rings (Ann. of Math. 86 (1967), 138–171).

    Article  MathSciNet  MATH  Google Scholar 

  19. S. Sakai, On a conjecture of Kaplansky (Tôhoku Math. J. 12 (1960), 31–33).

    Article  MathSciNet  MATH  Google Scholar 

  20. S. Sakai, Derivations of W*-algebras (Ann. of Math. 83 (1966), 273–279).

    Article  MathSciNet  MATH  Google Scholar 

  21. J. T. Schwartz, Two finite, non-hyperfinite, non-isomorphic factors (Comm. Pure Appl. Math. 16 (1963), 19–26).

    Article  MathSciNet  MATH  Google Scholar 

References (Books)

  1. J. Dixmier, "Les C*-algèbres et leurs représentations" (Gauthiers-Villars, Paris, 1964).

    MATH  Google Scholar 

  2. J. Dixmier, "Les algèbres d'opérateurs dans l'espace Hilbertien (algèbres de von Neumann)" (2nd edition, Gauthier-Villars, Paris, 1969).

    MATH  Google Scholar 

  3. F. P. Greenleaf, "Invariant means on topological groups" (van Nostrand, New York, 1969).

    MATH  Google Scholar 

  4. M. Takesaki, "Tomita's theory of modular Hilbert algebras and its applications (Lecture Notes in Math. 128, Springer, Berlin, 1970).

    MATH  Google Scholar 

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© 1972 Springer-Verlag

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Ringrose, J.R. (1972). Cohomology of operator algebras. In: Lectures on Operator Algebras. Lecture Notes in Mathematics, vol 247. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0058555

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  • DOI: https://doi.org/10.1007/BFb0058555

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-05729-1

  • Online ISBN: 978-3-540-37117-5

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