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An example of an asymptotically Hilbertian space which fails the approximation property
Author(s):
P.
G.
Casazza;
C.
L.
García;
W.
B.
Johnson
Journal:
Proc. Amer. Math. Soc.
129
(2001),
3017-3023.
MSC (2000):
Primary 46B20, 46B07, 46B28;
Secondary 46B99
Posted:
April 24, 2001
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Abstract:
Following Davie's example of a Banach space failing the approximation property (1973), we show how to construct a Banach space  which is asymptotically Hilbertian and fails the approximation property. Moreover, the space  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
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
Email:
johnson@math.tamu.edu
DOI:
10.1090/S0002-9939-01-06142-1
PII:
S 0002-9939(01)06142-1
Keywords:
Banach spaces,
weak Hilbert spaces,
asymptotically Hilbertian,
approximation property
Received by editor(s):
March 1, 2000
Posted:
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 of article:
Copyright
2001,
P. G. Casazza, C. L. García, and W. B. Johnson
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