Mathematische Annalen

, Volume 287, Issue 1, pp 509–514 | Cite as

On the compact non-nuclear operator problem

  • Kamil John
Article

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References

  1. 1.
    Davis, W., Johnson, W.B.: Compact, non-nuclear operators. Stud. Math.51, 81–85 (1974)Google Scholar
  2. 2.
    Diestel, J.: Sequences and series in Banach spaces. (Graduate texts in math. vol. 92) Berlin Heidelberg New York: Springer 1984Google Scholar
  3. 3.
    Grothendieck, A.: Produits tensoriels topologiques espaces nucléaires. Mem. Am. Math. Soc.16 (1955)Google Scholar
  4. 4.
    Grothendieck, A.: Résumé de la théorie métrique des produits tensoriels topologiques. Bol. Soc. Mat. São Paulo8, 1–79 (1956)Google Scholar
  5. 5.
    Jarchow, H.: On Hilbert-Schmidt spaces. Rend. Circ. Mat. Palermo (Suppl)II (2), 153–160 (1982)Google Scholar
  6. 6.
    Jarchow, H.: Locally convex spaces. Stuttgart: Teubner 1981Google Scholar
  7. 7.
    John, K.: Tensor products and nuclearity. Lect. Notes Math., Vol. 991, pp. 124–129 Berlin Heidelberg New York: Springer 1983Google Scholar
  8. 8.
    John, K.: Counterexample to a conjecture of Grothendieck. Math. Ann.265, 169–179 (1983)Google Scholar
  9. 9.
    John, K.: Tensor products of several spaces and nuclearity. Math. Ann.269, 333–356 (1984)Google Scholar
  10. 10.
    John, K.: Nuclearity and tensor products. Doĝa Tr. J. Math.10, 125–135 (1986)Google Scholar
  11. 11.
    John, K.: Some remarks on the compact non-nuclear operator problem. Lond. Math. Soc. Lect. Note Ser.150, 140–144 (1989)Google Scholar
  12. 12.
    John, K., Zizler, V.: Projections in dual weakly compactly generated Banach spaces. Stud. Math.49, 41–50 (1973)Google Scholar
  13. 13.
    Johnson, W.B.: On finite dimensional subspaces of Banach spaces with local unconditional structure. Stud. Math.51, 225–240 (1974)Google Scholar
  14. 14.
    Johnson, W.B., König, H., Maurey, B., Retherford, R.: Eigenvalues ofp-summing andl p-type operators in Banach spaces. J. Funct. Anal.32, 353–380 (1979)Google Scholar
  15. 15.
    Kalton, N.J.: Spaces of compact operators. Math. Ann.208, 267–278 (1974)Google Scholar
  16. 16.
    Lindenstrauss, J.: On non-separable reflexive Banach spaces. Bull. Am. Math. Soc.72, 967–970 (1966)Google Scholar
  17. 17.
    Lindenstrauss, J., Pelczyński, A.: Absolutely summing operators in ℒp-spaces and their application. Stud. Math.29, 275–326 (1968)Google Scholar
  18. 18.
    Lindenstrauss, J., Tzafriri, L.: Classical Banach spaces. I. Berlin Heidelberg New York: Springer 1977Google Scholar
  19. 19.
    Niculescu, C.P.: New progress on ℒ(E,F)=N 1(E,F). An. Univ. Craiova, Ser. Mat. Fiz.-Chim.6, 27–29 (1978)Google Scholar
  20. 20.
    Pietsch, A.: Nuclear locally convex spaces. Berlin Heidelberg New York: Springer 1972Google Scholar
  21. 21.
    Pietsch, A.: Operator ideals. Berlin: Deutscher Verlag der Wissenschaften 1978Google Scholar
  22. 22.
    Pisier, G.: Un théorème sur les opérateurs linéaires entre espaces de Banach qui se factorisent par un espace de Hilbert. Ann. Sci. Ec. Norm. Supér., IV. Sér.13, 23–43 (1980)Google Scholar
  23. 23.
    Pisier, G.: Counterexamples to a conjecture of Grothendieck. Acta. Math.151, 180–208 (1983)Google Scholar
  24. 24.
    Pisier, G.: Factorization of linear operators and geometry of Banach spaces. CBMS Regional conference, series n0 60, AMS, 1-154 (1986)Google Scholar
  25. 25.
    Singer, I.: Bases in Banach spaces. II. Berlin Heidelberg New York: Springer 1981Google Scholar
  26. 26.
    Stegall, C.P., Retherford, J.R.: Fully nuclear and completely nuclear operators with applications to ℒ1 and ℒ-spaces. Trans. Am. Math. Soc.163, 457–492 (1972)Google Scholar
  27. 27.
    Tseitlin, I.I.: On a particular case of the existence of a compact operator which is not nuclear. Funkts. Anal. Prilozh6, 102 (1979)Google Scholar
  28. 28.
    Tseitlin, I.I.: The extreme points of the unit ball of certain spaces of operators. Mat. Zametki20, 521–527 (1976)Google Scholar
  29. 29.
    Ruess, W., Stegall, Ch.: Extreme points in duals of operator spaces. Math. Ann.261, 535–546 (1982)Google Scholar

Copyright information

© Springer-Verlag 1990

Authors and Affiliations

  • Kamil John
    • 1
  1. 1.Mathematical InstituteCzechoslovak Academy of SciencesPraha 1Czechoslovakia

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