On Uniformly Finitely Extensible Banach spaces |
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| Authors: | Jesú s M.F. Castillo,Valentin Ferenczi,Yolanda Moreno |
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| Affiliation: | 1. Departamento de Matemáticas, Universidad de Extremadura, Avda de Elvas s/n, 06011 Badajoz, Spain;2. Departamento de Matemática, Instituto de Matemática e Estatística, Universidade de São Paulo, rua do Matão, 1010, 05508-090 São Paulo, SP, Brazil;3. Equipe d?Analyse Fonctionnelle, Institut de Mathématiques, Université Pierre et Marie Curie – Paris 6, Case 247, 4 place Jussieu, 75252 Paris Cedex 05, France;4. Departamento de Matemáticas, Escuela Politécnica de Cáceres, Universidad de Extremadura, Avda de la Universidad s/n, 07011 Cáceres, Spain |
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| Abstract: | We continue the study of Uniformly Finitely Extensible Banach spaces (in short, UFO) initiated in Moreno and Plichko (2009) [39] and Castillo and Plichko (2010) [18]. We show that they have the Uniform Approximation Property of Pe?czyński 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 c0(I) and ?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 ?2 spaces in the literature cannot be automorphic. |
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| Keywords: | Extension of operators B-convex Banach spaces Hereditarily Indecomposable spaces |
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