You don't provide enough info and how would you expect people to give you useful feedback? What is the intended function of the sliding door? What are the separated spaces for? Where are the doors? Windows? Traffic flow?

The diagram is not clear at all.

If the gap is only 4 ft wide, you can either put a aluminum door with black or green glass or just leave it as it is. You are not going to save that much of aircon because the other 7 ft is wall? You can also put in a top hanging sliding door as well.

You do not need aircon when you do work in your study???