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Proceedings of the American Mathematical Society

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

 
 

 

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
DOI: https://doi.org/10.1090/S0002-9939-1989-0984799-7
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.


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DOI: https://doi.org/10.1090/S0002-9939-1989-0984799-7
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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