If an astronaut dies in space, will there be any decomposition of his body by bacteria?
If he dies in his space suit, then yes, he would decompose, because he still has bacteria and such within his body that would decompose him. It would use up all of the oxygen, however, so the decomposition would become anaerobic very quickly, going from respiration to fermentation.
Radiation would not significantly affect the decomposition process. It would break up chemical bonds and such, but our deceased astronaut is more likely to collide with an object of some kind like a meteor before that would really break him up.
If our astronaut is not in his suit, then the vacuum would kill the bacteria decomposing him in fairly short order.
Source: UCSB Science Line