A fixed point free nonexpansive map
Dale E. Alspach · Proceedings of the American Mathematical Society · 1981
In this note we give an example of a weakly compact convex subset of L 1 [ 0 , 1 ] {L_1}[0,1] that fails to have the fixed point property for nonexpansive maps. This answers a long-standing question which was recently raised again by S. Reich [ 7 ].