Definition:Resolvent Set/Bounded Linear Operator

Definition
Let $\struct {X, \norm \cdot_X}$ be a Banach space over $\C$.

Let $A : X \to X$ be a linear operator.

Let:


 * $\map \rho A = \set {\lambda \in \C : A - \lambda I \text { is invertible with bounded inverse} }$

We call $\map \rho A$ the resolvent set of $A$.