Iam new in this field. I am reading a paper and have encoutered the following Lemma.
Let $u\in F_{1}.$ Then $Sp(u)=\{0, tr(u)\},$ where $F_{1}$ is the set of one-dimensional elements and tr(u) is the trace of $u.$ Can someone kindly help me with some hints on how I can use the Spectral mapping theorem for the proof to this Lemma. Thanking you in advance.