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

Cleon S. Barroso

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

Functional Analysis 2018-08-15 v2

Authors: Cleon S. Barroso

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 $\co$ .

Keywords

fixed point property banach spaces isomorphic to c0 james distortion theorem ramsey theorem spreading models weak compactness

Cite

@article{arxiv.1807.11614,
  title  = {On the fixed point property in Banach spaces isomorphic to $c_0$},
  author = {Cleon S. Barroso},
  journal= {arXiv preprint arXiv:1807.11614},
  year   = {2018}
}

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

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

Abstract

Keywords

Cite

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