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Transactions of the American Mathematical Society

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



Injective Banach spaces of continuous functions

Author: John Wolfe
Journal: Trans. Amer. Math. Soc. 235 (1978), 115-139
MSC: Primary 46E15; Secondary 46M10
MathSciNet review: 0461113
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Abstract: A description is given of the compact Hausdorff spaces S such that the Banach space $ C(S)$ of continuous functions on S is a $ {P_\lambda }$-space for $ \lambda < 3$ (under the assumption that S satisfies the countable chain condition). The existence of extension operators from $ C({X^\ast}\backslash X)$ to $ C({X^\ast})$ is examined under the assumption that $ C({X^\ast})$ is injective where $ {X^\ast}$ is some compactification of a locally compact extremally disconnected Hausdorff space X (if $ C(S)$ is injective, S is of this form). Some new examples of injective spaces $ C(S)$ are given.

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Keywords: $ {P_\lambda }$-space, injective Banach space, space of continuous functions, Gleason map, averaging operator
Article copyright: © Copyright 1978 American Mathematical Society

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