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 bounded linear operator.

Let:


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

where invertible is meant in the sense of a invertible bounded linear transformation.

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