The Lumer-Phillips theorem characterizes the infinitesimal generators of contraction semigroups.
A densely defined linear operator 
on a Banach space 
generates such a semigroup iff 
is a dissipative operator
and
 |
for some 
,
where 
is the identity operator. This range condition
says that 
is surjective. Equivalently, 
is an 
-dissipative operator.
