The resolvent set 
of a closed operator 
on a complex Banach space 
consists of the scalars 
for which 
maps the domain of 
bijectively
onto 
and has a bounded inverse,
 |
Here 
is the identity operator. For 
, the bounded
operator
 |
is called the resolvent operator of 
. The operator spectrum
of 
is the complement of 
in the complex plane.
Bounds on 
are central to the study of semigroup stability.
