Contractive projections in continuous function spaces

Lindberg, Karl

doi:10.1090/S0002-9939-1972-0306881-7

Contractive projections in continuous function spaces
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by Karl Lindberg PDF

Proc. Amer. Math. Soc. 36 (1972), 97-103 Request permission

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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