As part of my course on Functional Analysis in my 7th semester, I was required to present a topic that was an extension of the course. I chose to read up on annihilators of Banach spaces and characterize the conditions required for the sum of two closed subspaces of a Banach space to be closed. You know, just because.
The report assumes a basic understanding of Banach spaces and the knowledge of various versions of the Hahn-Banach theorem. It also uses a small fact from convex optimization theory. I’ve done my best to iron out typos and avoid mistakes. If you find any typos, mistakes or just want to talk about this topic, email me!