publication . Article . Preprint . 2013

on uniformly finitely extensible banach spaces

Castillo, Jesús M. F.; Ferenczi, Valentin; Moreno, Yolanda;
Open Access
  • Published: 16 Jul 2013 Journal: Journal of Mathematical Analysis and Applications, volume 410, pages 670-686 (issn: 0022-247X, Copyright policy)
  • Publisher: Elsevier BV
We continue the study of Uniformly Finitely Extensible Banach spaces (in short, UFO) initiated in Moreno-Plichko, \emph{On automorphic Banach spaces}, Israel J. Math. 169 (2009) 29--45 and Castillo-Plichko, \emph{Banach spaces in various positions.} J. Funct. Anal. 259 (2010) 2098-2138. We show that they have the Uniform Approximation Property of Pe\l czy\'nski and Rosenthal and are compactly extensible. We will also consider their connection with the automorphic space problem of Lindenstrauss and Rosenthal --do there exist automorphic spaces other than $c_0(I)$ and $\ell_2(I)$?-- showing that a space all whose subspaces are UFO must be automorphic when it is He...
arXiv: Mathematics::Functional AnalysisMathematics::General Topology
free text keywords: Applied Mathematics, Analysis, Mathematical analysis, Discrete mathematics, Minimax approximation algorithm, Indecomposable module, Linear subspace, Topology, Isomorphism, Interpolation space, Banach space, Lp space, Hilbert space, symbols.namesake, symbols, Mathematics, Mathematics - Functional Analysis
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