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

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- by P. G. Casazza, C. L. García and W. B. Johnson PDF
- Proc. Amer. Math. Soc.
**129**(2001), 3017-3023

## Abstract:

Following Davie’s example of a Banach space failing the approximation property (1973), 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.## References

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## Additional Information

**P. G. Casazza**- Affiliation: Department of Mathematics, University of Missouri-Columbia, Columbia, Missouri 65211
- MR Author ID: 45945
- Email: pete@math.missouri.edu
**C. L. García**- Affiliation: Department of Mathematics, Texas A&M University, College Station, Texas 77843–3368
- Email: clgarcia@math.tamu.edu
**W. B. Johnson**- Affiliation: Department of Mathematics, Texas A&M University, College Station, Texas 77843–3368
- MR Author ID: 95220
- Email: johnson@math.tamu.edu
- Received by editor(s): March 1, 2000
- Published electronically: April 24, 2001
- Additional Notes: The first author was supported by NSF grant DMS-970618.

The second and third authors were supported in part by NSF grants DMS-9623260, DMS-9900185, and by the Texas Advanced Research Program under Grant No. 010366-163. - Communicated by: N. Tomczak-Jaegermann
- © Copyright 2001 P. G. Casazza, C. L. García, and W. B. Johnson
- Journal: Proc. Amer. Math. Soc.
**129**(2001), 3017-3023 - MSC (2000): Primary 46B20, 46B07, 46B28; Secondary 46B99
- DOI: https://doi.org/10.1090/S0002-9939-01-06142-1
- MathSciNet review: 1840107