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

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

2000-06-19

arxiv.org/abs/math/0006134v2

Mathematics

Functional Analysis

7 pages

Scientific paper

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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