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Matematicheskie Zametki, 2020, Volume 108, Issue 2, Pages 252–259
DOI: https://doi.org/10.4213/mzm12677 (Mi mzm12677) 		 
A Banach Lattice Having the Approximation Property, but not Having the Bounded Approximation Property

O. I. Reinov

Saint Petersburg State University
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DOI: https://doi.org/10.4213/mzm12677
Abstract: 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.
Keywords: Banach lattice, basis, approximation property, bounded approximation property.
Received: 16.01.2020
English version:
Mathematical Notes, 2020, Volume 108, Issue 2, Pages 243–249
DOI: https://doi.org/10.1134/S0001434620070251
Bibliographic databases:
Document Type: Article
UDC: 517.983.27
Language: Russian
Citation: O. I. Reinov, “A Banach Lattice Having the Approximation Property, but not Having the Bounded Approximation Property”, Mat. Zametki, 108:2 (2020), 252–259; Math. Notes, 108:2 (2020), 243–249
Citation in format AMSBIB
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