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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The approximation property does not imply the bounded approximation property


Authors: T. Figiel and W. B. Johnson
Journal: Proc. Amer. Math. Soc. 41 (1973), 197-200
MSC: Primary 46B05; Secondary 47B10
MathSciNet review: 0341032
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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],


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1973-0341032-5
PII: S 0002-9939(1973)0341032-5
Keywords: Approximation property, nuclear operators
Article copyright: © Copyright 1973 American Mathematical Society