The approximation property of some vector valued Sobolev-Slobodeckij spaces - Carlos Bosch; Salvador Pérez-Esteva; Joaquín Motos (International Journal of Mathematics and Mathematical Sciences)
In this paper we consider the Sobolev-Slobodeckij spaces Wm,p(ℜn,E) where E is a strict (LF)-space, m∈(0,∞)\ℕ and p∈[1,∞). We prove that Wm,p(ℜn,E) has the approximation property provided E has it, furthermore if E is a Banach space with the strict approximation property then Wm,p(ℜn,E) has this property.