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Mathematics > Functional Analysis

Title: $\ell_1$ spreading models and FPP in Banach spaces with monotone Schauder basis

Authors: Cleon S. Barroso
(Submitted on 8 Feb 2023 (v1), last revised 20 Mar 2023 (this version, v3))
Abstract: The main result of this paper is a fixed point result relating the spreading model structure of Banach spaces and Schauder basis with not too large basis constant. As a striking consequence, we deduce that every super-reflexive space has the fixed point property thus solving a long-standing open question in metric fixed point theory.
Comments: The first statement on page 9 is not necessarily true. Roughly speaking, the problem is that the indices "i_s" and "r" are competing with each other and therefore what I believed to be immediate, as happens naturally in the case of a single index, and as can be seen in the proof of Theorem 6.7 of the FHHMZ reference, is in fact not immediate in the situation where double indices are involved
Subjects: Functional Analysis (math.FA)
Cite as: arXiv:2302.04323 [math.FA]
  (or arXiv:2302.04323v3 [math.FA] for this version)

Submission history

From: Cleon Barroso S. [view email]
[v1] Wed, 8 Feb 2023 20:37:50 GMT (18kb)
[v2] Thu, 16 Feb 2023 14:31:45 GMT (19kb)
[v3] Mon, 20 Mar 2023 19:28:56 GMT (0kb,I)
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