publication . Preprint . Article . 2013

On Uniformly Finitely Extensible Banach spaces

Jesús M.F. Castillo; Valentin Ferenczi; Yolanda Moreno;
Open Access English
  • Published: 16 Jul 2013
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 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...
Subjects
arXiv: Mathematics::Functional AnalysisMathematics::General Topology
free text keywords: ANÁLISE FUNCIONAL NÃO LINEAR, ESPAÇOS DE BANACH, Mathematics - Functional Analysis, 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
50 references, page 1 of 4

k X ǫjxjk1F/θ ≤ j

[1] G. Androulakis and K. Beanland, A hereditarily indecomposable asymptotic ℓ2 Banach space, Glasgow Math. J. 48 (2006) 503-532.

[2] G. Androulakis and Th. Schlumprecht, Strictly singular, non-compact operators exist on the space of Gowers and Maurey, J. London Math. Soc. (2) 64 (2001), no. 3, 655-674. [OpenAIRE]

[3] R. Anisca, On the ergodicity of Banach spaces with property (H). Extracta Math. 26 (2011), 165-171.

[4] S. Argyros, K. Beanland and Th. Raikoftsalis, A weak Hilbert space with few symmetries, C.R.A.S. Paris, ser I, 348 (2010) 1293-1296.

[5] S.A. Argyros and Deliyanni, Examples of asymptotically ℓ1 Banach spaces, Trans. Amer. Math. Soc. 349 (1997) 973-995.

[6] S.A. Argyros, D. Freeman, R. Haydon, E. Odell, Th. Raikoftsalis, Th. Schlumprecht and D. Zisimopoulou, Embedding uniformly convex spaces into spaces with very few operators, J. Funct. Anal. 262 (2012) 825-849. [OpenAIRE]

[7] S.A. Argyros and R.G. Haydon, A hereditarily indecomposable L∞-space that solve the scalarplus-compact problem, Acta Math. 206 (2011) 1-54. [OpenAIRE]

[8] S.A. Argyros and T. Raikoftsalis, The cofinal property of the reflexive indecomposable Banach spaces. To appear in Ann. Inst. Fourier (Grenoble).

[9] S. Argyros and A. Tollias, Methods in the theory of hereditarily indecomposable Banach spaces, Mem. Amer. Math. Soc. 806 (2004).

[10] A. Avil´es, F. Cabello, J. M. F. Castillo, M. Gonz´alez and Y. Moreno, On separably injective Banach spaces, Advances in Mathematics, 234 (2013), 192-216.

[11] A. Aviles and Y. Moreno, Automorphisms in spaces of continuous functions on Valdivia compacta, Topology Appl. 155 (2008) 2027-2030.

[12] P. G. Casazza and W. B. Johnson, An example of an asymptotically Hilbertian space which fails the approximation property, Proc. Amer. Math. Soc. 129 (2001) 3017-3023 [OpenAIRE]

[13] P. G. Casazza, N. J. Kalton, D. Kutzarova and M. Mastylo, Complex interpolation and complementably minimal spaces, Interaction between functional analysis, harmonic analysis, and probability (Columbia, MO, 1994), 135-143, Lecture Notes in Pure and Appl. Math., 175, Dekker, New York, 1996. [OpenAIRE]

[14] P.G. Casazza and N.J. Nielsen, The Maurey extension property for Banach spaces with the Gordon-Lewis property and related structures, Studia Math. 155 (2003) 1-21.

50 references, page 1 of 4
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publication . Preprint . Article . 2013

On Uniformly Finitely Extensible Banach spaces

Jesús M.F. Castillo; Valentin Ferenczi; Yolanda Moreno;