The search experience could really be improved by adding a selection criteria in front of the search bar to determine the scope of your search.
Now it you are in a space and you search it searches the entire database. Personally and think many would agree that it would be better if you can determine the scope of your search. So for example I open a space, by default the search will change to search to only include assets within the selected space. If you want to search all assets you change the setting to all assets.
See below a quick visual representation.
Customer support service by UserEcho