I've run into a few problems in which reflexivity of a Banach space is given as a hypothesis. These problems are sometimes of the type where the banach space is specific/concrete, and sometimes it is just any Banach space. To me, reflexivity seems to be a hard condition to use. Is there an easy list of tricks to use this hypothesis? For example, does reflexivity imply any more tangible results via a standard theorem from functional analysis? An example of the type of answer I'm looking for is "Reflexivity often allows one to use the uniform boundedness principle" or "Reflexivity implies that the unit ball is weakly compact." But one of the reasons I'm asking these questions is because I feel I'm missing some other tricks that get used in functional analysis because I'm asked the question
"Show that every C* algebra that is reflexive as a Banach space is finite dimensional" and I feel that I simply don't know enough tricks/theorems to do this. (I could also use hints on this specific question, which might go some ways in revealing to me more tricks for reflexivity in general.)