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Extension of operators from subspaces of \(c_ 0(\Gamma)\) into C(K) spaces. (English) Zbl 0697.46006

By a result of Lindenstrauß and Pelczynski for every operator T from a subspace of \(c_ 0\) to CK and \(\epsilon >0\) there exists an extension to all of \(c_ 0\) with norm not greater than \(\| T\| (1+\epsilon)\). Using this and a decomposition technique it is proved in the present paper that \(c_ 0\) may be replaced by \(c_ 0(\Gamma)\) for arbitrary index sets \(\Gamma\). It is also shown that \(\epsilon =0\) is not admissible, even in the case of countable \(\Gamma\).
Reviewer: E.Behrends

MSC:

46B25 Classical Banach spaces in the general theory
46B03 Isomorphic theory (including renorming) of Banach spaces
47B99 Special classes of linear operators
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