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Mathematics > Functional Analysis

arXiv:1807.11614 (math)
This paper has been withdrawn by Cleon Barroso S.
[Submitted on 31 Jul 2018 (v1), last revised 13 Aug 2018 (this version, v2)]

Title:On the fixed point property in Banach spaces isomorphic to $c_0$

Authors:Cleon S. Barroso
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Abstract:We prove that every Banach space containing a subspace isomorphic to $\co$ fails the fixed point property. The proof is based on an amalgamation approach involving a suitable combination of known results and techniques, including James's distortion theorem, Ramsey's combinatorial theorem, Brunel-Sucheston spreading model techniques and Dowling, Lennard and Turett's fixed point methodology employed in their characterization of weak compactness in $\co$.
Comments: Unfortunately there is a gap in the proof of Theorem 3.2. The diagonal argument fails to prove inequality (iii), as it only works though spreading models
Subjects: Functional Analysis (math.FA)
Cite as: arXiv:1807.11614 [math.FA]
  (or arXiv:1807.11614v2 [math.FA] for this version)
  https://doi.org/10.48550/arXiv.1807.11614

Submission history

From: Cleon Barroso S. [view email]
[v1] Tue, 31 Jul 2018 00:26:17 UTC (11 KB)
[v2] Mon, 13 Aug 2018 23:40:46 UTC (1 KB) (withdrawn)
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