Compact and weakly compact disjointness preserving operators on spaces   of differentiable functions
  A pair of functions defined on a set X with values in a vector space E is said to be disjoint if at least one of the functions takes the value 0 at every point in X. An operator acting between vector-valued function spaces is disjointness preserving if it maps disjoint functions to disjoint functions. We characterize compact and weakly compact disjointness preserving operators between spaces of Banach space-valued differentiable functions. 
Denny H. Leung and Ya-Shu Wang
math.FA