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Injective Banach Spaces of Continuous Functions

John Wolfe
Transactions of the American Mathematical Society
Vol. 235 (Jan., 1978), pp. 115-139
DOI: 10.2307/1998210
Stable URL: http://www.jstor.org/stable/1998210
Page Count: 25
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Injective Banach Spaces of Continuous Functions
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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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