© 2015 Elsevier Inc. Let X be a Banach space and let Y be a closed subspace of a Banach space Z. Let ? be a tensor norm. Our main result is as follows. Assume that X^* or Z^* has the approximation property. If there is a bounded linear extension operator from Y^* to Z^*, then any bounded linear operator T:X?Y is ?-nuclear whenever T is ?-nuclear from X to Z. Using this result, we characterize the space Cp(?,X) (respectively, UCp(?,X)) of continuous functions from a compact Hausdorff space ? into a Banach space X whose range is p-compact (respectively, unconditionally p-compact).