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Extension of operators from subspaces of $ c\sb 0(\Gamma)$ into $ C(K)$ spaces

Authors: W. B. Johnson and M. Zippin
Journal: Proc. Amer. Math. Soc. 107 (1989), 751-754
MSC: Primary 46B25; Secondary 47A20, 47B38
MathSciNet review: 984799
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Abstract: It is shown that for every $ \varepsilon > 0$, every bounded linear operator $ T$ from a subspace $ X$ of $ {c_0}\left( \Gamma \right)$ into a $ C\left( K \right)$ space has an extension $ {\mathbf{T}}$ from $ {c_0}\left( \Gamma \right)$ into the $ C\left( K \right)$ space such that $ \left\Vert {\mathbf{T}} \right\Vert \leq \left( {1 + \varepsilon } \right)\left\Vert T \right\Vert$. Even when $ \Gamma $ is countable, $ T$ is compact, and $ X$ has codimension 1 in $ {c_0}$, the " $ \varepsilon $" cannot be replaced by 0. These results answer questions raised by J. Lindenstrauss and A. Pełczynski in 1971.

References [Enhancements On Off] (What's this?)

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Keywords: Hahn-Banach extensions, operators into $ C\left( K \right)$, continuous selections, extension of operators
Article copyright: © Copyright 1989 American Mathematical Society

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