A Banach Lattice Having the Approximation Property, but not Having the Bounded Approximation Property

The first example of a Banach space with the approximation property but without the bounded approximation property was given by Figiel and Johnson in 1973. We give the first example of a Banach lattice with the approximation property but without the bounded approximation property. As a consequence,...

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Bibliographic Details
Published in:Mathematical Notes 2020-07, Vol.108 (1-2), p.243-249
Main Author: Reinov, O. I.
Format: Article
Language:English
Subjects:
14/34
639/766/189
639/766/530
639/766/747
Approximation
Banach spaces
Integrals
Mathematical analysis
Mathematics
Mathematics and Statistics
Operators (mathematics)
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Summary:The first example of a Banach space with the approximation property but without the bounded approximation property was given by Figiel and Johnson in 1973. We give the first example of a Banach lattice with the approximation property but without the bounded approximation property. As a consequence, we prove the existence of an integral operator (in the sense of Grothendieck) on a Banach lattice which is not strictly integral.
ISSN:0001-4346
1067-9073
1573-8876
DOI:10.1134/S0001434620070251