A Banach space in which every injective operator is surjective (Q2854235)
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scientific article; zbMATH DE number 6216279
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A Banach space in which every injective operator is surjective |
scientific article; zbMATH DE number 6216279 |
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A Banach space in which every injective operator is surjective (English)
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18 October 2013
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\(C(K)\) space
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injective operator
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surjective operator
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The authors answer a question of \textit{A. Haïly, A. Kaidi} and \textit{A. Rodríguez Palacios} [Isr. J. Math. 177, 349-368 (2010; Zbl 1205.47005)]. More precisely, they prove that there is an infinite-dimensional Banach space \(X\) such that whenever a bounded linear operator \(T: X \to X\) is injective, then it is an isomorphism onto \(X\). Moreover, \(X\) is of the form \(C(K)\).
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