# The Compact Approximation Property does not imply the Approximation Property

Studia Mathematica (1992)

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

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topWillis, 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

top- [C] P. Casazza, personal communication.
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- [D2] A. M. Davie, The Banach approximation problem, J. Approx. Theory 13 (1975), 392-394. Zbl0299.46019
- [Da] M. M. Day, Uniform convexity in factor and conjugate spaces, Ann. of Math. 45 (1944), 375-385. Zbl0063.01058
- [E] P. Enflo, A counterexample to the approximation property in Banach spaces, Acta Math. 130 (1973), 309-317. Zbl0267.46012
- [G] A. Grothendieck, Produits tensoriels topologiques et espaces nucléaires, Mem. Amer. Math. Soc. 16 (1955).
- [GW] N. Grønbæk and G. Willis, Approximate identities in Banach algebras of compact operators, Canad. Math. Bull., to appear. Zbl0794.46017
- [LT1] J. Lindenstrauss and L. Tzafriri, Classical Banach Spaces I, Springer, Berlin 1977. Zbl0362.46013
- [LT2] J. Lindenstrauss and L. Tzafriri, Classical Banach Spaces II, Springer, Berlin 1979. Zbl0403.46022
- [S] C. Samuel, Bounded approximate identities in the algebra of compact operators on a Banach space, Proc. Amer. Math. Soc., to appear. Zbl0785.46026
- [Sz] A. Szankowski, Subspaces without approximation property, Israel J. Math. 30 (1978), 123-129. Zbl0384.46008

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