A complementary universal conjugate Banach space and its relation to the approximation problem |
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Authors: | William B Johnson |
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Institution: | (1) Ohio State University, 43210 Columbus, Ohio |
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Abstract: | LetC
1=(ΣG
n
)
l
1, where (G
n
) is a sequence which is dense (in the Banach-Mazur sense) in the class of all finite dimensional Banach spaces. IfX is a separable Banach space, thenX
* is isometric to a subspace ofC
1
*
=(ΣG
n
*
)
m
which is the range of a contractive projection onC
1
*
. Separable Banach spaces whose conjugates are isomorphic toC
1
*
are classified as those spaces which contain complemented copies of C1. Applications are that every Banach space has the metric] approximation property (m.] a.p., in short) iff (ΣG
n
*
)
m
does, and if there is a space failing the m.a.p., thenC
1 can be equivalently normed to fail the m.a.p.
The author was supported in part by NSF GP 28719. |
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Keywords: | |
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