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.References
- Nelson Dunford and Jacob T. Schwartz, Linear Operators. I. General Theory, Pure and Applied Mathematics, Vol. 7, Interscience Publishers, Inc., New York; Interscience Publishers Ltd., London, 1958. With the assistance of W. G. Bade and R. G. Bartle. MR 0117523
- Joram Lindenstrauss, Extension of compact operators, Mem. Amer. Math. Soc. 48 (1964), 112. MR 179580
- Joram Lindenstrauss and Daniel E. Wulbert, On the classification of the Banach spaces whose duals are $L_{1}$ spaces, J. Functional Analysis 4 (1969), 332–349. MR 0250033, DOI 10.1016/0022-1236(69)90003-2
- Daniel E. Wulbert, Some complemented function spaces in $C(X)$, Pacific J. Math. 24 (1968), 589–602. MR 223868
Additional Information
- © Copyright 1972 American Mathematical Society
- 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