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Banach Spaces of Almost Universal Complemented Disposition
Quarterly Journal of Mathematics ( IF 0.7 ) Pub Date : 2019-12-10 , DOI: 10.1093/qmathj/haz045
Jesús M F Castillo 1 , Yolanda Moreno 1
Affiliation  

Abstract
We introduce and study the notion of space of almost universal complemented disposition (a.u.c.d.) as a generalization of Kadec space. We show that every Banach space with separable dual is isometrically contained as a $1$-complemented subspace of a separable a.u.c.d. space and that all a.u.c.d. spaces with $1$-finite dimensional decomposition (FDD) are isometric and contain isometric $1$-complemented copies of every separable Banach space with $1$-FDD. We then study spaces of universal complemented disposition (u.c.d.) and provide different constructions for such spaces. We also consider spaces of u.c.d. with respect to separable spaces.


中文翻译:

几乎全补充配置的Banach空间

摘要
我们介绍和研究几乎普遍的补充性配置(aucd)的空间概念,作为Kadec空间的推广。我们证明,每个具有可分离对偶的Banach空间都是等距包含为可分离aucd空间的$ 1 $补充子空间,并且所有具有$ 1 $有限维分解(FDD)的aucd空间都是等距的,并且包含等距的$ 1 $补充的副本每个可分离的Banach空间为$ 1 $ -FDD。然后,我们研究通用补充处置(ucd)的空间,并为此类空间提供不同的构造。我们还考虑了ucd相对于可分离空间的空间。
更新日期:2020-04-17
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