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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Contractive projections in continuous function spaces


Author: Karl Lindberg
Journal: Proc. Amer. Math. Soc. 36 (1972), 97-103
MSC: Primary 46E15
DOI: https://doi.org/10.1090/S0002-9939-1972-0306881-7
MathSciNet review: 0306881
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Abstract: Let $ C(K)$ be the Banach space of real-valued continuous functions on a compact Hausdorff space with the supremum norm and let X be a closed subspace of $ C(K)$ which separates points of K. Necessary and sufficient conditions are given for X to be the range of a projection of norm one in $ C(K)$. It is shown that the form of a projection of norm one is determined by a real-valued continuous function which is defined on a subset of K and which satisfies conditions imposed by X. When there is a projection of norm one onto X, it is shown that there is a one-to-one correspondence between the continuous functions which satisfy the conditions imposed by X and the projections of norm one onto X.


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DOI: https://doi.org/10.1090/S0002-9939-1972-0306881-7
Keywords: Contractive projection, extreme points, involutive homeomorphism, isometry
Article copyright: © Copyright 1972 American Mathematical Society