\begin{definition}[Definition:Imaginary Part (Linear Operator)]
Let $\HH$ be a Hilbert space over $\C$.
Let $A \in \map B \HH$ be a bounded linear operator.
Then the '''imaginary part of $A$''' is the Hermitian operator:
:$\Im A := \dfrac 1 {2 i} \paren {A - A^*}$
\end{definition}