A weak vector-valued Banach-Stone theorem (Q2845427)
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scientific article; zbMATH DE number 6203312
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A weak vector-valued Banach-Stone theorem |
scientific article; zbMATH DE number 6203312 |
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A weak vector-valued Banach-Stone theorem (English)
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30 August 2013
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space of vector-valued continuous functions
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Banach-Stone type theorems
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0.9143111
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0.91199625
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0.90850115
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0.90289026
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0.9006274
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The authors prove a vector-valued version of a result of \textit{B. Cengiz} [Proc. Am. Math. Soc. 72, 105--108 (1978; Zbl 0397.46022)], which says that two locally compact Hausdorff spaces \(X, Y\) have the same cardinality if the Banach spaces \(C_0(X)\) and \(C_0(Y)\) are isomorphic.NEWLINENEWLINELet \(E\) be a Banach space having non-trivial cotype and suppose \(E^\ast\) has the Radon-Nikodym property or \(E\) is separable. If \(C_0(X,E)\) is isomorphic to \(C_0(Y,E)\), the authors show that either \(X, Y\) are finite sets or they have the same cardinality.
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