The Compact Approximation Property does not imply the Approximation Property

1992/05/04 by George A. Willis, Willis, George A.
Decision Sciences · Mathematics · #Advanced Banach Space Theory #Advanced Topology and Set Theory #FOS: Mathematics #Functional Analysis (math.FA) #Fuzzy and Soft Set Theory #math.FA

paper · pdf · doi:10.48550/arxiv.math/9205203

arxiv created 1992/05/04 · openalex publication_date 1992/05/04 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

It is shown how to construct, given a Banach space which does not have the approximation property, another Banach space which does not have the approximation property but which does have the compact approximation property.

Related

• On Banach spaces without the approximation property
• Banach spaces without approximation properties of type p
• The Dual Form of the Approximation Property for a Banach Space and a Subspace
• Self-Induced Compactness in Banach Spaces
• Retractions and the bounded approximation property in Banach spaces