Mathematische Annalen

, Volume 298, Issue 1, pp 349–371 | Cite as

Weak compactness in the dual of a C*-algebra is determined commutatively

  • H. Pfitzner
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References

  1. 1.
    Akemann, Ch.A.: The general Stone-Weierstraß problem. J. Funct. Anal.4, 277–294 (1969)Google Scholar
  2. 2.
    Akemann, Ch.A., Dodds, P.G., Gamlen, J.L.B.: Weak compactness in the dual space of a C*-algebra. J. Funct. Anal.10, 446–450 (1972)Google Scholar
  3. 3.
    Ando, T.: Convergent sequences of finitely additive measures. Pac. J. Math.11, 395–404 (1961)Google Scholar
  4. 4.
    Bonsall, F.F., Duncan, J.: Numerical ranges of operators on normed spaces and of elements of normed algebras (London Mathematical Society Lecture Note Series 2) Cambridge: Cambridge University Press 1971Google Scholar
  5. 5.
    Bourgain, J.: H is a Grothendieck space. Stud. Math.75, 193–216 (1983)Google Scholar
  6. 6.
    Bourgain, J.: The Dunford-Pettis property for the ball-algebras, the polydisc-algebras and the Sobolev spaces. Stud. Math.77, 245–253 (1984)Google Scholar
  7. 7.
    Chu, C.H., Iochum, B.: Complementation of Jordan triples in von Neumann algebras. Proc. Am. Math. Soc.108, 19–24 (1990)Google Scholar
  8. 8.
    Dashiel, F.K.: Nonweakly compact operators from order-Cauchy complete C(S) lattices, with applications to Baire classes. Trans. Am. Math. Soc.266, 397–413 (1981)Google Scholar
  9. 9.
    Diestel, J.: A survey of results related to the Dunford-Pettis property. In: Proc. Conf. on integration, topology and geometry in linear spaces, (Contemporary Mathematics, A.M.S., vol. 2, p. 15–60) Rhode Island: Providence 1979Google Scholar
  10. 10.
    Diestel, J.: Sequences and series in Banach spaces. Berlin Heidelberg New York: Springer 1984Google Scholar
  11. 11.
    Doran, R.S., Belfi, V.A.: Characterizations of C*-algebras. New York Basel: Marcel Dekker 1986Google Scholar
  12. 12.
    Dunford, N., Schwartz, J.T.: Linear operators. Part 1: General theory. New York: Interscience Publishers 1958Google Scholar
  13. 13.
    Godefroy, G.: Sous-espaces bien disposés deL 1-Applications. Trans. Am. Math. Soc.286, 227–249 (1984)Google Scholar
  14. 14.
    Godefroy, G., Saab, P.: Quelques espaces de Banach ayant les propriétés (V) ou (V*) de A. Pełczyński. C.R. Acad. Sci., Paris, Sér. 1303, 503–506 (1986)Google Scholar
  15. 15.
    Godefroy, G., Saab, P.: Weakly unconditionally convergent series inM-ideals. Math. Scand.64, 307–318 (1989)Google Scholar
  16. 16.
    Grothendieck, A.: Sur les applications linéaires faiblement compactes d'espaces du type C(K). Can. J. Math.5, 129–173 (1953)Google Scholar
  17. 17.
    Harmand, P., Werner, D., Werner, W.:M-ideals in Banach spaces and Banach algebras. (Lect. Notes Math., vol. 1547) Berlin Heidelberg New York: Springer 1993Google Scholar
  18. 18.
    Haydon, R.: A non-reflexive Grothendieck space that does not containl . Isr. J. Math.40, 65–73 (1981)Google Scholar
  19. 19.
    James, R.C.: Uniformly non-square Banach spaces. Ann. Math., II. Ser.80, 542–550 (1964)Google Scholar
  20. 20.
    Leung, D.H.: Uniform convergence of operators and Grothendieck spaces with the Dunford-Pettis property. Math. Z.197, 21–32 (1988)Google Scholar
  21. 21.
    Leung, D.H.: Weak convergence in higher duals of Orlicz spaces. Proc. Am. Math. Soc.102, 797–800 (1988)Google Scholar
  22. 22.
    Lindenstrauss, J., Tzafriri, L.: Classical Banach spaces. (Lect. Notes. Math., vol. 338) Berlin Heidelberg New York: Springer 1973Google Scholar
  23. 23.
    Lindenstrauss, J., Tzafriri, L.: Classical Banach spaces I. Berlin Heidelberg New York: Springer 1977Google Scholar
  24. 24.
    Lindenstrauss, J., Tzafriri, L.: Classical Banach spaces II. Berlin Heidelberg New York: Springer 1979Google Scholar
  25. 25.
    Pedersen, G.K.: C*-algebras and their automorphism groups. London New York San Francisco: Academic Press 1979Google Scholar
  26. 26.
    Pedersen, G.K.: Analysis now. (Grad. Texts Math., vol. 118) Berlin Heidelberg New York, Springer 1988Google Scholar
  27. 27.
    Pelczyński, A.: Banach spaces on which every unconditionally converging operator is weakly compact. Bull. Pol. Acad. Sci., Math.10, 641–648 (1962)Google Scholar
  28. 28.
    Räbiger, F.: Beiträge zur Strukturtheorie der Grothendieckräume. Sitzungsberichte der Heidelberger Akademie der Wissenschaften 1985Google Scholar
  29. 29.
    Seever, G.L.: Measures onF-spaces. Trans. Am. Math. Soc.133, 267–280 (1968)Google Scholar
  30. 30.
    Takesaki, M.: Theory of operator algebras I. Berlin Heidelberg New York: Springer 1979Google Scholar
  31. 31.
    Talagrand, M.: Un nouveau C(K) qui possède la propriété de Grothendieck. Isr. J. Math.37, 181–191 (1980)Google Scholar
  32. 32.
    Upmeier, H.: Symmetrie Banach manifolds and Jordan C*-algebras. Amsterdam New York Oxford: North-Holland 1985Google Scholar

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© Springer-Verlag 1994

Authors and Affiliations

  • H. Pfitzner
    • 1
  1. 1.Mathematisches InstitutLudwig-Maximilian-Universität MünchenMünchenGermany

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