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Some Structures Related to Metric Projections in Orlicz Spaces

Bor-Luh LinZhongrui Shi — 1999

Colloquium Mathematicae

We discuss k-rotundity, weak k-rotundity, C-k-rotundity, weak C-k-rotundity, k-nearly uniform convexity, k-β property, C-I property, C-II property, C-III property and nearly uniform convexity both pointwise and global in Orlicz function spaces equipped with Luxemburg norm. Applications to continuity for the metric projection at a given point are given in Orlicz function spaces with Luxemburg norm.

Characterizations of L 1 -predual spaces by centerable subsets

Yanzheng DuanBor-Luh Lin — 2007

Commentationes Mathematicae Universitatis Carolinae

In this note, we prove that a real or complex Banach space X is an L 1 -predual space if and only if every four-point subset of X is centerable. The real case sharpens Rao’s result in [, Proc. Amer. Math. Soc. (2002), no. 9, 2593–2598] and the complex case is closely related to the characterizations of L 1 -predual spaces by Lima [, Israel J. Math. (1976), no. 1, 59–72].

Ball remotal subspaces of Banach spaces

Pradipta BandyopadhyayBor-Luh LinT. S. S. R. K. Rao — 2009

Colloquium Mathematicae

We study Banach spaces X with subspaces Y whose unit ball is densely remotal in X. We show that for several classes of Banach spaces, the unit ball of the space of compact operators is densely remotal in the space of bounded operators. We also show that for several classical Banach spaces, the unit ball is densely remotal in the duals of higher even order. We show that for a separable remotal set E ⊆ X, the set of Bochner integrable functions with values in E is a remotal set in L¹(μ,X).

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