I am currently taking a course on functional analysis and we discussed spectral theory. I am having a lot of trouble with the following type of exercises
Given a linear operator $T: X \rightarrow X$ that is defined like (bla). Calculate the spectrum and resolvent set.
Does there exist a general approach to such problems? A good general strategy to solve such exercises? Because it seems to me that for every problem there could be a whole different strategy.
Sincerely, a confused undergrad. Thanks in advance!