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 Bosch,1 Salvador Pérez-Esteva,1 and Joaquín Motos2

1Instituto de Matemáticas, U.N.A.M., Area de la Investigación Científica, Ciudad Universitaria, Mexico D.F. 04510, Mexico
2Departamento de Matemática Aplicada, Universidad Politécnica de Valencia, Camino de Vera s/n, Valencia 46022, Spain

Received 2 February 1990; Revised 2 March 1991

Copyright © 1992 Carlos Bosch et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.