Sectorial operator

A sectorial operator is a type of linear operator in functional analysis that generalizes the concept of self-adjoint operators. Sectorial operators arise in the study of partial differential equations and the theory of semigroups of operators. They are particularly important in the context of evolution equations and their solutions. An operator \( A \) on a Banach space \( X \) is said to be sectorial if it has a sector in the complex plane where its spectrum lies.