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- W2949062472 abstract "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 Pel 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 Hereditarily Indecomposable (HI), and a Hilbert space when it is either locally minimal or isomorphic to its square. We will finally show that most HI --among them, the super-reflexive HI space constructed by Ferenczi-- and asymptotically $ell_2$ spaces in the literature cannot be automorphic." @default.
- W2949062472 created "2019-06-27" @default.
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- W2949062472 date "2013-07-16" @default.
- W2949062472 modified "2023-09-26" @default.
- W2949062472 title "On Uniformly finitely extensible Banach spaces" @default.
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