ArticleOriginal scientific text

Title

The Compact Approximation Property does not imply the Approximation Property

Authors 1

Affiliations

  1. Mathematics Research Section, School of Mathematical Sciences, The Australian National University, GPO Box 4, Canberra, Act, Australia

Abstract

It is shown how to construct, given a Banach space which does not have the approximation property, another Banach space which does not have the approximation property but which does have the compact approximation property.

Bibliography

  1. [C] P. Casazza, personal communication.
  2. [D1] A. M. Davie, The approximation problem for Banach spaces, Bull. London Math. Soc. 5 (1973), 261-266.
  3. [D2] A. M. Davie, The Banach approximation problem, J. Approx. Theory 13 (1975), 392-394.
  4. [Da] M. M. Day, Uniform convexity in factor and conjugate spaces, Ann. of Math. 45 (1944), 375-385.
  5. [E] P. Enflo, A counterexample to the approximation property in Banach spaces, Acta Math. 130 (1973), 309-317.
  6. [G] A. Grothendieck, Produits tensoriels topologiques et espaces nucléaires, Mem. Amer. Math. Soc. 16 (1955).
  7. [GW] N. Grønbæk and G. Willis, Approximate identities in Banach algebras of compact operators, Canad. Math. Bull., to appear.
  8. [LT1] J. Lindenstrauss and L. Tzafriri, Classical Banach Spaces I, Springer, Berlin 1977.
  9. [LT2] J. Lindenstrauss and L. Tzafriri, Classical Banach Spaces II, Springer, Berlin 1979.
  10. [S] C. Samuel, Bounded approximate identities in the algebra of compact operators on a Banach space, Proc. Amer. Math. Soc., to appear.
  11. [Sz] A. Szankowski, Subspaces without approximation property, Israel J. Math. 30 (1978), 123-129.
Pages:
99-108
Main language of publication
English
Received
1991-10-18
Accepted
1992-04-14
Published
1992
Exact and natural sciences