Lumer–Phillips theorem
In mathematics, the Lumer–Phillips theorem, named after Günter Lumer and Ralph Phillips, is a result in the theory of strongly continuous semigroups that gives a necessary and sufficient condition for a linear operator in a Banach space to generate a contraction semigroup. == Statement of the theorem == Let A be a linear operator defined on a linear subspace D(A) of the Banach space X. Then A generates a contraction semigroup if and only if D(A) is dense in X, A is dissipative, and A − λ0I is surjective for some λ0> 0, where I denotes the identity operator.