On extensions of c₀-valued operators

Original · EN

We study pairs of Banach spaces (X,Y), with Y⊂ X, for which the thesis of Sobczyk's theorem holds, namely, such that every bounded c₀-valued operator defined in Y extends to X. We are mainly concerned with the case when X is a C(K) space and Y≡ 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 every bounded c₀-valued operator defined in C(L) extends to C(K).