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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

$ C(\alpha )$ preserving operators on $ C(K)$ spaces


Author: John Wolfe
Journal: Trans. Amer. Math. Soc. 273 (1982), 705-719
MSC: Primary 46E15; Secondary 46B25
DOI: https://doi.org/10.1090/S0002-9947-1982-0667169-9
MathSciNet review: 667169
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Abstract: Let $ A:C(K) \to X$ be a bounded linear operator where $ K$ is a compact Hausdorff space and $ X$ is a separable Banach space. Sufficient conditions are given for $ A$ to be an isomorphism (into) when restricted to a subspace $ Y$ of $ C(K)$, such that $ Y$ is isometrically isomorphic to a space $ C(\alpha )$ of continuous functions on the space of ordinal numbers less than or equal to the countable ordinal $ \alpha $.


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DOI: https://doi.org/10.1090/S0002-9947-1982-0667169-9
Article copyright: © Copyright 1982 American Mathematical Society

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