# The property WORTH* and the weak fixed point property

Article

Dalby, Tim. 2014. "The property WORTH* and the weak fixed point property."

*Journal of Nonlinear and Convex Analysis.*15 (5), pp. 919-927.Article Title | The property WORTH* and the weak fixed point property |
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ERA Journal ID | 261 |

Article Category | Article |

Authors | |

Author | Dalby, Tim |

Journal Title | Journal of Nonlinear and Convex Analysis |

Journal Citation | 15 (5), pp. 919-927 |

Number of Pages | 9 |

Year | 2014 |

Place of Publication | Yokohama, Japan |

ISSN | 1345-4773 |

1880-5221 | |

Web Address (URL) | http://www.ybook.co.jp/online2/jncav15.html |

Abstract | A Banach space, $X$, has the weak fixed point property (w-FPP) if every nonexpansive mapping, $T$, on every weak compact convex nonempty subset, $C$, has a fixed point. A Banach space, $X^*$, has WORTH* if for every weak* null sequence $(x^*_n)$ and every $x^* \in X^*$, \[\limsup_n\|x^*_n-x^*\|=\limsup_n\|x^*_n+x^*\|.\] A new proof is given of the recent result that WORTH* implies the weak fixed point property. |

Keywords | properties WORTH; WORTH*; weak fixed point property; 1-unconditional basis |

ANZSRC Field of Research 2020 | 490408. Operator algebras and functional analysis |

490201. Algebraic structures in mathematical physics | |

Public Notes | Files associated with this item cannot be displayed due to copyright restrictions. |

Byline Affiliations | Open Access College |

Institution of Origin | University of Southern Queensland |

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https://research.usq.edu.au/item/q289y/the-property-worth-and-the-weak-fixed-point-property

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