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

• Autorzy: T. Figiel , W. B. Johnson
• Języki publikacji: 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.

Kategorie tematyczne

• 46B20: Geometry and structure of normed linear spaces
• 46B03: Isomorphic theory (including renorming) of Banach spaces
• 46B15: Summability and bases

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2015
• Tom: 231
• Numer: 3
• Strony: 287-292

Daty

wydano

2015

Twórcy

autor

T. Figiel

• Institute of Mathematics, Polish Academy of Sciences, Branch in Gdańsk, Wita Stwosza 57, 80-952 Gdańsk, Poland

autor

W. B. Johnson

• Department of Mathematics, Texas A&M University, College Station, TX 77843-3368, U.S.A.

Identyfikatory

DOI

10.4064/sm8367-2-2016