On Banach spaces \(Y\) for which \(B(C (\Omega), Y)= K(C (\Omega), Y)\) (Q1901069)

Let \(\Omega\) be a compact Hausdorff space. In this paper, we give some necessary conditions and some sufficient conditions on a Banach space \(Y\) in order that all continuous operators from the space \(C(\Omega)\) into \(Y\) are compact. We prove that for a nonscattered compact Hausdorff space \(\Omega\) and for \(Y\) belonging to a large class of Banach spaces, all continuous operators from \(C(\Omega)\) into \(Y\) are compact if and only if all continuous operators from \(\ell^2\) into \(Y\) are compact.