User:Caliburn/s/fa/1
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Theorem
Let $\struct {\HH, \innerprod \cdot \cdot_\HH}$ be a Hilbert space.
Let $A : \HH \to \HH$ be a bounded linear operator.
Let $A^* : \HH \to \HH$ be the adjoint of $A$.
Let $\map \sigma A$ be the spectrum of $A$.
Let $\map \sigma {A^*}$ be the spectrum of $A^*$.
Then:
- $\lambda \in \map \sigma A$ if and only if $\overline \lambda \in \map \sigma {A^*}$