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Results in Mathematics

, Volume 21, Issue 3–4, pp 299–312 | Cite as

The problem of topologies of grothendieck for quojections

  • Juan Carlos Diaz
  • Giorgio Metafune
Results in Mathematics
  • 5 Downloads

Keywords

Banach Space Approximation Property Twisted Space Unconditional Basis Fixed Class 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    F. Bastin, Weighted spaces of continuous functions, Bull. Soc. Roy. Sci. Liège, 59 (1990), 1–81.MATHGoogle Scholar
  2. 2.
    G. Bennet, L.E. Dor, V. Goodman, W.B. Johnson, C. M. Newmann, On uncomplemented subspaces of L, 1p 2, Israel J. Math. 26 (1977), 178–187.MathSciNetCrossRefGoogle Scholar
  3. 3.
    K.D. Bierstedt, J. Bonet, Dual density condition in (DF)-spaces, II, Bull. Soc. Roy. Sci. Liège, 57 (1988) 567–589.MathSciNetMATHGoogle Scholar
  4. 4.
    K.D. Biertedt, R. Meise, W. Summers, Köthe sets and Köthe sequence spaces, pp. 27-91 in: Functional Analysis, Holomorphy and Approximation Theory, North-Holland, Math. Studies 71, 1982.Google Scholar
  5. 5.
    J. Bonet, S. Dierolf, On (LB)-spaces of Moscatelli type, DOGA Tr. Math. J. 13,1 (1989), 933.MathSciNetGoogle Scholar
  6. 6.
    J. Bonet, S. Dierolf, Fréchet spaces of Moscatelli type, Rev. Matem. Univ. Complutense Madrid, 2, no suplementario (1989) 59–75.MathSciNetMATHGoogle Scholar
  7. 7.
    J. Bonet, J.C. Diaz, The problem of topologies of Grothendieck and the class of Fréchet T-spaces, Math. Nachr. (to appear).Google Scholar
  8. 8.
    J. Bonet, J.Taskinen, Quojections and the problem of topologies of Grothendieck, Note di Maternatica (Köthe memorial voume) to appear.Google Scholar
  9. 9.
    J. Bonet, A. Defant, A. Galbis, Tensor product of Fréchet or (DF)-spaces with a Banach space, J. Math. Anal, and Appl. (to appear).Google Scholar
  10. 10.
    J. Bonet, J.C. Diaz, J. Taskinen, Tensor stability of Fréchet and (DF)-spaces,preprint, 1990.Google Scholar
  11. 11.
    P. Domanski, Twisted spaces of continuous functions, preprint, 1989.Google Scholar
  12. 12.
    A. Grothendieck, Produits tensoriels topologiques et espaces nucléaires, Mem. Amer. Math. Soc. 16, 1955.Google Scholar
  13. 13.
    G. Köthe, Topological Vector Spaces I, II,Springer Berlin, Heidelberg, New York, 1969, 1979.Google Scholar
  14. 14.
    J. Lindenstrauss, A. Pelczynski, Absolutely summing operators in Lp -spaces and their applications, Studia Math. 29 (1968), 275–326.MathSciNetMATHGoogle Scholar
  15. 15.
    G. Metafune. V.B. Moscatelli, Quojections and Prequojections, pp. 235–254 in Advances in the Theory of Fréchet spaces, K uwer Academic Publishers, 1989.CrossRefGoogle Scholar
  16. 16.
    G. Metafune, V.B. Moscatelli, On twisted Fréchet and (LB)-spaces, Proc. Amer. Math. Soc. 108,1 (1990), 145–150.MathSciNetMATHGoogle Scholar
  17. 17.
    V.B. Moscatelli, Fréchet spaces without continuous norms and without bases, Bull. London Math. Soc. 12 (1980), 63–66.MathSciNetMATHCrossRefGoogle Scholar
  18. 18.
    J. Taskinen, Counterexamples to “problème des topologies” of Grothendieck, Ann. Acad. Sci. Fenn., Ser. A I Math. Dissertationes 63 (1986).Google Scholar
  19. 19.
    J. Taskinen, The projective tensor product of Fréchet Montel spaces, Studia Math. 91 (1988) 17–30.MathSciNetMATHGoogle Scholar
  20. 20.
    J. Taskinen, (FBa)- and (FBB)-spaces, Math. Z. 198 (1988) 339–365.MathSciNetMATHCrossRefGoogle Scholar

Copyright information

© Birkhäuser Verlag, Basel 1992

Authors and Affiliations

  • Juan Carlos Diaz
    • 1
  • Giorgio Metafune
    • 2
  1. 1.Departamento de Matemáticas, E.T.S.I. AgrónomosUniversidad de CórdobaCordobaSpain
  2. 2.Dipartimento di MatematicaII UniversitéItaly

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