\begin{definition}[Definition:Resolvent Set of Bounded Linear Operator]
Let $\struct {X, \norm \cdot}$ be a Banach space over $\C$. 
Let $A : X \to X$ be a bounded linear operator.
Let $I : X \to X$ be the identity mapping on $X$. 
Let $\map \rho A$ be the set of $\lambda \in \C$ such that $A - \lambda I$ is invertible in the sense of a bounded linear transformation
We call $\map \rho A$ the '''resolvent set''' of $A$.
\end{definition}