Space elevator may kill

Travellers on the space elevator may be killed by the radiation in the van Allen belts around the earth between 1000 and 20000 km away from the earth. Because the elevator travels at 200 mph, passengers will be exposed for days to the radiation, whereas rocket travellers go much faster. I wonder how they solved this problem for the free fall dude who took a balloon up to the edge of space and jumped out with a hole in his suit?