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PROPERTIES $(U\~{A}_2)^*$ AND $(W\~{A}_2)$ IN ORLICZ SEQUENCE SPACES AND SOME OF THEIR CONSEQUENCES

Cui, Yunan and Hudzik, Henryk and Sims, Brailey PROPERTIES $(U\~{A}_2)^*$ AND $(W\~{A}_2)$ IN ORLICZ SEQUENCE SPACES AND SOME OF THEIR CONSEQUENCES. Journal of Mathematical Analysis and Applications . (Submitted)

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    Abstract

    In this paper, we introduce a new geometric property $(U\~{A}_2)$ and we show that if a separable Banach space has this property, then both $X$ and its dual $X^*$ have the weak fixed point property. We also prove that a uniformly Gateaux differentiable Banach space has property $(U\~{A}_2)$ and that if $X^*$ has property $(U\~{A}_2)^*$, then $X$ has the $(UKK)$-property. Criteria for Orlicz spaces to have the properties $(UA^\epsilon_2), (UA^\epsilon_2)^*$ and $(NUS*$) are given.

    Item Type: Article
    Uncontrolled Keywords: Orlicz space, Property $(A^\epsilon_2), Fixed point property,(UKK)-property, Weak fixed point property, The weak Banach-Saks property.
    Subjects: 46-xx Functional analysis > 46Bxx Normed linear spaces and Banach spaces; Banach lattices
    47-xx Operator theory > 47Hxx Nonlinear operators and their properties
    Faculty: UNSPECIFIED
    Depositing User: Mr Christopher Maitland
    Date Deposited: 13 Apr 2011 12:21
    Last Modified: 13 Apr 2011 12:21
    URI: https://docserver.carma.newcastle.edu.au/id/eprint/869

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