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Normal structure and weakly normal structure of Orlicz spaces

Shutao Chen; Yanzheng Duan — 1991

Commentationes Mathematicae Universitatis Carolinae

Every Orlicz space equipped with Orlicz norm has weak sum property, therefore, it has weakly normal structure and fixed point property. A criterion of sum property also of normal structure for such spaces is given as well, which shows that every Orlicz space has isonormal structure.

A note on Schroeder-Bernstein Property and Primary Property of Orlicz function spaces

Yanzheng Duan; Shutao Chen — 1998

Commentationes Mathematicae Universitatis Carolinae

It is shown in the note that every reflexive Orlicz function space has the Schroeder-Bernstein Property and the Primary Property.

Characterizations of $L^{1}$ -predual spaces by centerable subsets

Yanzheng Duan; Bor-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].

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Currently displaying 1 – 3 of 3

Normal structure and weakly normal structure of Orlicz spaces

A note on Schroeder-Bernstein Property and Primary Property of Orlicz function spaces

Characterizations of L 1 -predual spaces by centerable subsets

Characterizations of $L^{1}$ -predual spaces by centerable subsets