The approximation property of some vector valued Sobolev-Slobodeckij spaces

In this paper we consider the Sobolev-Slobodeckij spaces Wm,p( ￠ n,E) where E is a strict (LF)-space, m ￠ (0, ￠ ) ￠ and p ￠ [1, ￠ ). We prove that Wm,p( ￠ n,E) has the approximation property provided E has it, furthermore if E is a Banach space with the strict approximation property then Wm,p( ￠ n,E) has this property.