Double-dual types over the Banach space C(K)
Let K be a compact Hausdorff space and C(K) the Banach space of all real-valued continuous functions on K, with the sup-norm. Types over C(K) (in the sense of Krivine and Maurey) can be uniquely represented by pairs (ℓ,u) of bounded real-valued functions on K, where ℓ is lower semicontinuous, u is u...
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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2005-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/IJMMS.2005.2533 |
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| Summary: | Let K be a compact Hausdorff space and C(K) the Banach space
of all real-valued continuous functions on K, with the sup-norm.
Types over C(K) (in the sense of Krivine and Maurey) can be
uniquely represented by pairs (ℓ,u) of bounded real-valued
functions on K, where ℓ is lower semicontinuous, u is upper semicontinuous, ℓ≤u, and ℓ(x)=u(x) for all
isolated points x of K. A condition that characterizes the pairs (ℓ,u) that represent double-dual types over C(K) is given. |
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| ISSN: | 0161-1712 1687-0425 |