一个渐近希尔伯特空间不具有逼近性质的例子
An example of an asymptotically Hilbertian space which fails the approximation property
摘要：
继Davie的例子，一个巴拿赫空间失败的逼近性质[D]，我们展示了如何构建一个巴拿赫空间E这是渐近希尔伯特和失败的逼近性质。此外，证明了空间E是具有无条件基的空间的一个子空间，该空间“几乎”是一个弱希尔伯特空间，并且可以表示为两个子空间的直和，这两个子空间的所有子空间都具有逼近性质。
英文摘要：
Following Davie's example of a Banach space failing the approximation property [D], we show how to construct a Banach space E which is asymptotically Hilbertian and fails the approximation property. Moreover, the space E is shown to be a subspace of a space with an unconditional basis which is ``almost'' a weak Hilbert space and which can be written as the direct sum of two subspaces all of whose subspaces have the approximation property.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
