Czechoslovak Mathematical Journal

, Volume 49, Issue 3, pp 607–616 | Cite as

U-ideals of factorable operators

  • Kamil John


We suggest a method of renorming of spaces of operators which are suitably approximable by sequences of operators from a given class. Further we generalize J. Johnsons's construction of ideals of compact operators in the space of bounded operators and observe e.g. that under our renormings compact operators are u-ideals in the: space of 2-absolutely summing operators or in the space of operators factorable through a Hilbert space.

factorization of linear operators u-ideal approximation properties unconditional basis 


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  1. [E,J]
    G. Emmanuele, K. John: Some remarks on the position of the space \({\mathcal{K}}\) (X, Y) inside the space \({\mathcal{W}}\) (X, Y). New Zealand J. Math. 26(2) (1997), 183-189.Google Scholar
  2. [F]
    J. H. Fourie: Projections on operator duals. Quaestiones Math. 21 (1998), 11-18.Google Scholar
  3. [G,K,S]
    G. Godefroy, N. J. Kalton, P. D. Saphar: Unconditional ideals in Banach spaces. Studia Math. 104(1) (1993), 13-59.Google Scholar
  4. [H,W,W]
    P. Harmand, D. Werner, W. Werner: M-ideals in Banach Spaces and Banach Algebras. Lecture Notes in Math., 1547, Springer, Berlin, 1993.Google Scholar
  5. [J1]
    K. John: On the space \({\mathcal{W}}\) (P, P *) of compact operators on Pisier space P. Note di Matematica 12 (1992), 69-75.Google Scholar
  6. [J2]
    K. John: On a result of J. Johnson. Czechoslovak Math. Journal 45 (1995), 235-240.Google Scholar
  7. [Jo]
    J. Johnson: Remarks on Banach spaces of compact operators. J. Funct. Analysis 32 (1979), 304-311.Google Scholar
  8. [Ka]
    N. J. Kalton: Spaces of compact operators. Math. Annalen 208 (1974), 267-278.Google Scholar
  9. [Li]
    Å. Lima: Property (wM *) and the unconditional metric approximation property. Studia Math. 113(3) (1995), 249-263.Google Scholar
  10. [LT,I]
    J. Lindenstrauss, L. Tzafriri: Classical Banach Spaces, Sequence Spaces. EMG 92 Springer Verlag (1977).Google Scholar
  11. [LT,II]
    J. Lindenstrauss, L. Tzafriri: Classical Banach Spaces, Function Spaces. EMG 97 Springer Verlag (1979).Google Scholar
  12. [Pie]
    A. Pietsch: Operator ideals. Berlin, Deutscher Verlag der Wissenschaften, 1978.Google Scholar
  13. [Pi]
    J. Pisier: Counterexamples to a conjecture of Grothendieck. Acta mat. 151 (1983), 180-208.Google Scholar
  14. [Ru]
    W. Ruess: Duality and Geometry of spaces of compact operators. Functional Analysis: Surveys and Recent Results III. Math. Studies 90, North Holland, 1984, pp. 59-78.Google Scholar

Copyright information

© Mathematical Institute, Academy of Sciences of Czech Republic 1999

Authors and Affiliations

  • Kamil John
    • 1
  1. 1.Mathematical Institute of Czech Academy of SciencesPraha 1Czech Republic

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