The Compact Approximation Property does not imply the Approximation Property

George Willis

Studia Mathematica (1992)

  • Volume: 103, Issue: 1, page 99-108
  • ISSN: 0039-3223

Abstract

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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.

How to cite

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Willis, George. "The Compact Approximation Property does not imply the Approximation Property." Studia Mathematica 103.1 (1992): 99-108. <http://eudml.org/doc/215938>.

@article{Willis1992,
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.},
author = {Willis, George},
journal = {Studia Mathematica},
keywords = {compact approximation property},
language = {eng},
number = {1},
pages = {99-108},
title = {The Compact Approximation Property does not imply the Approximation Property},
url = {http://eudml.org/doc/215938},
volume = {103},
year = {1992},
}

TY - JOUR
AU - Willis, George
TI - The Compact Approximation Property does not imply the Approximation Property
JO - Studia Mathematica
PY - 1992
VL - 103
IS - 1
SP - 99
EP - 108
AB - 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.
LA - eng
KW - compact approximation property
UR - http://eudml.org/doc/215938
ER -

References

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  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. Zbl0267.46013
  3. [D2] A. M. Davie, The Banach approximation problem, J. Approx. Theory 13 (1975), 392-394. Zbl0299.46019
  4. [Da] M. M. Day, Uniform convexity in factor and conjugate spaces, Ann. of Math. 45 (1944), 375-385. Zbl0063.01058
  5. [E] P. Enflo, A counterexample to the approximation property in Banach spaces, Acta Math. 130 (1973), 309-317. Zbl0267.46012
  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. Zbl0794.46017
  8. [LT1] J. Lindenstrauss and L. Tzafriri, Classical Banach Spaces I, Springer, Berlin 1977. Zbl0362.46013
  9. [LT2] J. Lindenstrauss and L. Tzafriri, Classical Banach Spaces II, Springer, Berlin 1979. Zbl0403.46022
  10. [S] C. Samuel, Bounded approximate identities in the algebra of compact operators on a Banach space, Proc. Amer. Math. Soc., to appear. Zbl0785.46026
  11. [Sz] A. Szankowski, Subspaces without approximation property, Israel J. Math. 30 (1978), 123-129. Zbl0384.46008

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