Space Warfare?

So you hear about spy satelittes being up in space. US spy satts above Chinese airspace and vice versa. Since no one had jurisdiction over space, what stops China have blowing up US spy sats and vice versa?

>>1

The satellite is US property.  EXPENSIVE US property.  I would imagine its like if you park your car in a store's parking lot, the store/property owner doesn't get to smash up your car.