This is an announcement for the paper "The Dual Form of the Approximation Property for a Banach Space and a Subspace" by T. Figiel and W. B. Johnson.

Abstract: Given a Banach space X and a subspace Y, the pair (X,Y) is said to have the approximation property (AP) provided there is a net of finite rank bounded linear operators on X all of which leave the subspace Y invariant such that the net converges uniformly on compact subsets of X to the identity operator. The main result is an easy to apply dual formulation of this property. Applications are given to three space properties; in particular, if X has the approximation property and its subspace Y is script L-infinity, then X/Y has the approximation property.

Archive classification: math.FA

Mathematics Subject Classification: Primary: 46B20, 46B28

Submitted from: johnson@math.tamu.edu

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1508.01212

or

http://arXiv.org/abs/1508.01212