Question
Suppose $L: U \rightarrow U$ has an adjoint $L^*: U \rightarrow U$. (a) Show that $L+L^*$ is self-adjoint.(b) Show that $L \circ L^*$ is self-adjoint.
Step 1
An operator $M: U \rightarrow U$ is self-adjoint if $M^* = M$. We need to show this property for both $L + L^*$ and $L \circ L^*$. Show more…
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