User:Caliburn/s/fa/1

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:


 * $\lambda \in \map \sigma A$ $\overline \lambda \in \map \sigma {A^*}$