Can I cast a spell multiple times in one round across different investigators if I trade it?
A component can only be used once per turn. 


  Although an investigator cannot perform a component action from a
  single component more than once each round, he can perform component
  actions of different components


It's not a specific 'investigator' but 'any' investigator that cannot use the component more than once.

So the "use" of a card kind of "sticks" to the card and cannot be used by another investigator.