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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)


On a theorem of a Pełczyński

Author: John L. B. Gamlen
Journal: Proc. Amer. Math. Soc. 44 (1974), 283-285
MSC: Primary 46B99
MathSciNet review: 0341036
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Abstract: If $ Y$ is a weakly complete Banach space, and $ X$ is a Banach space with separable dual, then every continuous linear operator from $ {C_X}(K)$ to $ Y$ must be weakly compact. Here $ {C_X}(K)$ denotes the space of continuous functions on the compact Hausdorff space $ K$, having values in $ X$.

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Additional Information

PII: S 0002-9939(1974)0341036-3
Keywords: Weakly compact operators
Article copyright: © Copyright 1974 American Mathematical Society