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

O. I. Reinov

Saint Petersburg State University

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.

UDC: 517.983.27

Received: 16.01.2020

DOI: 10.4213/mzm12677

 English version: Mathematical Notes, 2020, 108:2, 243–249

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