The dual form of the approximation property for a Banach space and a subspace Academic Article uri icon

abstract

  • Instytut Matematyczny PAN, 2015. 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. In particular, if the pair (X, Y) has the AP then X, Y , and the quotient space X/Y have the classical Grothendieck AP. 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 L, then X/Y has the approximation property.

published proceedings

  • Studia Mathematica

author list (cited authors)

  • Figiel, T., & Johnson, W. B.

citation count

  • 3

complete list of authors

  • Figiel, T||Johnson, WB

publication date

  • January 2016