International Journal of Mathematics and Mathematical Sciences
Volume 15 (1992), Issue 3, Pages 425-433
doi:10.1155/S0161171292000577

The approximation property of some vector valued Sobolev-Slobodeckij spaces

Carlos Bosch1 , Salvador Pérez-Esteva1 and Joaquín Motos3

1Instituto de Matemáticas, U.N.A.M., Area de la Investigación Científica, Ciudad Universitaria, Mexico D.F. 04510, Mexico
 3Departamento de Matemática Aplicada, Universidad Politécnica de Valencia, Camino de Vera s/n, Valencia 46022, Spain

Abstract

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.