The proportional UAP characterizes weak Hilbert spaces

1990/12/31 by William B. Johnson, Johnson, William B., Gilles Pisier +1
Computer Science · Mathematics · #46B15 #46E30 #Advanced Banach Space Theory #Approximation Theory and Sequence Spaces #FOS: Mathematics #Functional Analysis (math.FA) #Optimization and Variational Analysis #math.FA #msc:46B15 #msc:46E30

paper · pdf · doi:10.48550/arxiv.math/9201220

arxiv created 1990/12/31 · openalex publication_date 1990/12/31 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that a Banach space has the uniform approximation property with proportional growth of the uniformity function iff it is a weak Hilbert space.

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• An example of an asymptotically Hilbertian space which fails the approximation property
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