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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On the kernel of a Markov projection on $ C(X)$


Author: Robert E. Atalla
Journal: Proc. Amer. Math. Soc. 93 (1985), 685-689
MSC: Primary 47B38; Secondary 47A65, 47B55
MathSciNet review: 776203
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Abstract: Let $ X$ be a compact metric space and $ L$ a closed linear subspace of $ C(X)$, the real valued continuous functions on $ X$. We give necessary and sufficient conditions of an algebraic nature for $ L$ to be the kernel of a Markov projection $ P$ on $ C(X)$. We also characterize compact spaces for which our result holds as those for which the Borsuk-Dugundji simultaneous extension theorem holds.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1985-0776203-5
PII: S 0002-9939(1985)0776203-5
Keywords: Markov projection, $ C(X)$, averaging operator, positive Borel measure
Article copyright: © Copyright 1985 American Mathematical Society