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An example of an asymptotically Hilbertian space which fails the approximation property

P. G. Casazza·C. L. Garcia·W. B. Johnson
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Abstract

Following Davie's example of a Banach space failing the approximation property [D], we show how to construct a Banach space E which is asymptotically Hilbertian and fails the approximation property. Moreover, the space E is shown to be a subspace of a space with an unconditional basis which is ``almost'' a weak Hilbert space and which can be written as the direct sum of two subspaces all of whose subspaces have the approximation property.

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P. G. Casazza, C. L. Garcia, W. B. Johnson. 2000-09-20. An example of an asymptotically Hilbertian space which fails the approximation property. https://arxiv.org/abs/math/0006134

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