The dual form of the approximation property for a Banach space and a subspace
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Publication:2804304
DOI10.4064/SM8367-2-2016zbMATH Open1368.46023arXiv1508.01212OpenAlexW2964185723MaRDI QIDQ2804304
Author name not available (Why is that?)
Publication date: 28 April 2016
Published in: (Search for Journal in Brave)
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.
Full work available at URL: https://arxiv.org/abs/1508.01212
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