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A Banach Lattice Having the Approximation Property, but not Having the Bounded Approximation Property
Mathematical Notes ( IF 0.6 ) Pub Date : 2020-07-01 , DOI: 10.1134/s0001434620070251
O. I. Reinov

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.

中文翻译:

具有逼近性质但不具有有界逼近性质的巴拿赫格

Figiel 和 Johnson 在 1973 年给出了具有近似性质但没有有界近似性质的 Banach 空间的第一个例子。我们给出了具有近似性质但没有有界近似性质的 Banach 格的第一个例子。因此,我们证明了在不是严格积分的 Banach 格上存在积分算子(在 Grothendieck 的意义上)。
更新日期:2020-07-01
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