The Approximation Property Does Not Imply the Bounded Approximation Property

descriptionPublicationkeyboard_double_arrow_right Article , Other literature type 01 Jan 1973Publisher:JSTORJournal:Proceedings of the American Mathematical Society, volume 41, page 197 (issn: 0002-9939,

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Authors: Figiel, T.; Johnson, W. B.;

doi: 10.2307/2038840 , 10.1090/s0002-9939-1973-0341032-5

The Approximation Property Does Not Imply the Bounded Approximation Property

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Abstract

There is a Banach space which has the approxi- mation 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).

Keywords

Linear operators belonging to operator ideals (nuclear, \(p\)-summing, in the Schatten-von Neumann classes, etc.), Summability and bases; functional analytic aspects of frames in Banach and Hilbert spaces

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