What does having ‘the’ before ownership in the second sentence indicate? When to use ‘the’ if I want to use ‘the’ before ownership?
There are a lot of compound verbs with take + an abstract noun without an article + preposition. For example:
take notice of
take offence at
take heed of
take care of
take exception to
take time to
When the complement is definite, you might expect the abstract to need the in front of it; but in fact these are all idiomatic without the.
Some of them can also be used with the: you can indeed take the ownership of something, and take the time to do something; but most of them can't.