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• # Artykuł - szczegóły

## Studia Mathematica

2015 | 231 | 3 | 287-292

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

EN

### Abstrakty

EN
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.

287-292

wydano
2015

### Twórcy

autor
• Institute of Mathematics, Polish Academy of Sciences, Branch in Gdańsk, Wita Stwosza 57, 80-952 Gdańsk, Poland
autor
• Department of Mathematics, Texas A&M University, College Station, TX 77843-3368, U.S.A.