Injective Banach spaces of continuous functions

Wolfe, John

doi:10.1090/S0002-9947-1978-0461113-4

Injective Banach spaces of continuous functions
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Trans. Amer. Math. Soc. 235 (1978), 115-139 Request permission

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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Some

Banach spaces

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