The approximation property does not imply the bounded approximation property

Figiel, T.; Johnson, W. B.

doi:10.1090/S0002-9939-1973-0341032-5

The approximation property does not imply the bounded approximation property
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by T. Figiel and W. B. Johnson

Proc. Amer. Math. Soc. 41 (1973), 197-200

DOI: https://doi.org/10.1090/S0002-9939-1973-0341032-5

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Abstract:

There is a Banach space which has the approximation property but fails the bounded approximation property. The space can be chosen to have separable conjugate, hence there is a nonnuclear operator on the space which has nuclear adjoint. This latter result solves a problem of Grothendieck [2],

References

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Collected letters