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Proceedings of the American Mathematical Society

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

 

 

Linear extensions and linear liftings in subspaces of $ C(X)$


Author: Eggert Briem
Journal: Proc. Amer. Math. Soc. 58 (1976), 85-93
MSC: Primary 46E25
DOI: https://doi.org/10.1090/S0002-9939-1976-0458149-X
MathSciNet review: 0458149
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Abstract: If $ X$ is a compact Hausdorff space, if $ B$ is a closed subspace of $ C(X)$ and if $ F$ is a closed subset of $ X$, conditions are given which ensure the existence of a linear extension operator of norm 1 from the restriction space $ B{\vert _F}$ to $ B$.


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DOI: https://doi.org/10.1090/S0002-9939-1976-0458149-X
Keywords: Linear extension, $ M$-set, $ M$-ideal, linear inverse, metric approximation property
Article copyright: © Copyright 1976 American Mathematical Society