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

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.

authors

• Johnson, William

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 2015

publisher

• Institute of Mathematics, Polish Academy of Sciences  Publisher

published in

• Studia Mathematica  Journal

keywords

• Approximation Property For Pairs
• Three-space Property

Digital Object Identifier (DOI)

• 10.4064/sm8367-2-2016

start page

• 287

end page

• 292

volume

• 231

issue

• 3

URL

• http%3A%2F%2Fdx.doi.org%2F10.4064%2Fsm8367-2-2016