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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Injective Banach spaces of continuous functions
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by John Wolfe PDF
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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Additional Information
  • © Copyright 1978 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 235 (1978), 115-139
  • MSC: Primary 46E15; Secondary 46M10
  • DOI: https://doi.org/10.1090/S0002-9947-1978-0461113-4
  • MathSciNet review: 0461113