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2 results

  • MORE ON THE ARENS REGULARITY OF $B(X)$

  • Part of
  • R. FAAL, H. R. EBRAHIMI VISHKI
  • Journal:
    Bulletin of the Australian Mathematical Society / Volume 94 / Issue 2 / October 2016
    Published online by Cambridge University Press:
    01 March 2016, pp. 296-303
    Print publication:
    October 2016
    • Article
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  • We focus on a question raised by Daws [‘Arens regularity of the algebra of operators on a Banach space’, Bull. Lond. Math. Soc.36 (2004), 493–503] concerning the Arens regularity of $B(X)$, the algebra of operators on a Banach space $X$. Among other things, we show that $B(X)$ is Arens regular if and only if $X$ is ultrareflexive.

  • The weak drop property on closed convex sets

  • Part of
  • Pei-Kee Lin, Xintai Yu
  • Journal:
    Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics / Volume 56 / Issue 1 / February 1994
    Published online by Cambridge University Press:
    09 April 2009, pp. 125-130
    Print publication:
    February 1994
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  • Recall a closed convex set C is said to have the weak drop property if for every weakly sequentially closed set A disjoint from C there exists x ∈ A such that co({x} ∩ C) ∪ A = {x}. Giles and Kutzarova proved that every bounded closed convex set with the weak drop property is weakly compact. In this article, we show that if C is an unbounded closed convex set of X with the weak drop property, then C has nonempty interior and X is a reflexive space.