Banach spaces of almost universal complemented disposition
Functional Analysis
2019-06-18 v3
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 -complemented subspace of a separable a.u.c.d. space and that all a.u.c.d. spaces with -FDD are isometric and contain isometric -complemented copies of every separable Banach space with -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.
Cite
@article{arxiv.1708.02431,
title = {Banach spaces of almost universal complemented disposition},
author = {Jesús M. F. Castillo and Yolanda Moreno},
journal= {arXiv preprint arXiv:1708.02431},
year = {2019}
}