THREE-SPACE PROBLEM FOR SOME APPROXIMATION PROPERTIES

Abstract

Suppose that M is a closed subspace of a Banach space X such that M(perpendicular to) is complemented in the dual space X*, where M(perpendicular to) = {x* is an element of X* : x*(m) = 0 for all m is an element of M}. Godefroy and Saphar [4] study the three-space problem for the approximation properties on (X, M). In this paper, we extend some of their results and solve the three-space problem for the weak bounded approximation property on (X, M), which was introduced in Lima and Oja [10].