Geodesic
A Banach Lattice Having the Approximation Property, but not Having the Bounded Approximation Property
Matematičeskie zametki, Tome 108 (2020) no. 2, pp. 252-259

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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. 
@article{MZM_2020_108_2_a8,
     author = {O. I. Reinov},
     title = {A {Banach} {Lattice} {Having} the {Approximation} {Property,} but not {Having} the {Bounded} {Approximation} {Property}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {252--259},
     publisher = {mathdoc},
     volume = {108},
     number = {2},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2020_108_2_a8/}
}
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O. I. Reinov. A Banach Lattice Having the Approximation Property, but not Having the Bounded Approximation Property. Matematičeskie zametki, Tome 108 (2020) no. 2, pp. 252-259. http://geodesic.mathdoc.fr/item/MZM_2020_108_2_a8/