A note on Schroeder-Bernstein Property and Primary Property of Orlicz function spaces
It is shown in the note that every reflexive Orlicz function space has the Schroeder-Bernstein Property and the Primary Property.
Normal structure and weakly normal structure of Orlicz spaces
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.
Characterizations of -predual spaces by centerable subsets
In this note, we prove that a real or complex Banach space is an -predual space if and only if every four-point subset of 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 -predual spaces by Lima [, Israel J. Math. (1976), no. 1, 59–72].
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