Resolvent of an operator ($R(z,A)=(zI-A{)}^{-1}$)

For a closed linear operator $A$, the resolvent is the bounded inverse $(zI-A{)}^{-1}$ when $z$ lies in the resolvent set of an operator. This definition includes unbounded $A$. It specializes to the resolvent of an element when $A$ is an element of a Banach algebra.