The Proportional Uap Characterizes Weak Hilbert Spaces

The Proportional Uap Characterizes Weak Hilbert Spaces

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

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Bibliographic Details
Published in:Journal of the London Mathematical Society Vol. s2-44; no. 3; pp. 525 - 536
Main Authors: Johnson, W. B., Pisier, G.
Format: Journal Article
Language:English
Published: London Oxford University Press 01-12-1991
Hodgson
Subjects:
Exact sciences and technology
Functional analysis
Mathematical analysis
Mathematics
Sciences and techniques of general use
Equivalence theorem
Banach space
Online Access:Get full text
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Description
Summary:We prove that a Banach space has the uniform approximation property with proportional growth of the uniformity function if and only if it is a weak Hilbert space.
Bibliography:istex:4F7B9A31147AFF854E76655AD5E7063321A06C85
ArticleID:s2-44.3.525
ark:/67375/HXZ-GJJTZHCN-4
ISSN:0024-6107
1469-7750
DOI:10.1112/jlms/s2-44.3.525