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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: <!– MATH ${P_\lambda }$ –> <IMG WIDTH="29" HEIGHT="38" ALIGN="MIDDLE" BORDER="0" SRC="images/img1.gif" ALT="${P_\lambda }$">-space, injective Banach space, space of continuous functions, Gleason map, averaging operator
Article copyright: © Copyright 1978 American Mathematical Society