In mathematics, more precisely in operator theory, a sectorial operator is a linear operator on a Banach space whose spectrum in an open sector in the complex plane and whose resolvent is uniformly bounded from above outside any larger sector.
Such operators might be unbounded.
Sectorial operators have applications in the theory of elliptic and parabolic partial differential equations.
be a Banach space.
be a (not necessarily bounded) linear operator on
, we define the open sector and set
is called sectorial with angle
ψ ∈ ( ω , π )
The set of sectorial operators with angle