1 Every Nonreflexive Subspace of L 1 [ 0 , 1 ] Fails the Fixed Point Property
نویسندگان
چکیده
The main result of this paper is that every non-reflexive subspace Y of L 1 [0, 1] fails the fixed point property for closed, bounded, convex subsets C of Y and nonexpansive (or contractive) mappings on C. Combined with a theorem of Maurey we get that for subspaces Y of L 1 [0, 1], Y is reflexive if and only if Y has the fixed point property. For general Banach spaces the question as to whether reflexivity implies the fixed point property and the converse question are both still open.
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