This is an announcement for the paper "On extensions of $c_0$-valued operators" by Claudia Correa and Daniel V. Tausk.

Abstract: We study pairs of Banach spaces $(X,Y)$, with $Y\subset X$, for which the thesis of Sobczyk's theorem holds, namely, such that every bounded $c_0$-valued operator defined in $Y$ extends to $X$. In this case, we say that $Y$ has the $c_0$-extension property in $X$. We are mainly concerned with the case when $X$ is a $C(K)$ space and $Y\equiv C(L)$ is a Banach subalgebra of $C(K)$. The main result of the article states that, if $K$ is a compact line and $L$ is countable, then $C(L)$ has the $c_0$-extension property in $C(K)$.

Archive classification: math.FA

Mathematics Subject Classification: 46B20, 46E15, 54F05

Remarks: 16 pages

Submitted from: tausk@ime.usp.br

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1211.4830

or

http://arXiv.org/abs/1211.4830