The Lumer-Phillips theorem says that a densely defined operator generates a contraction C0-semigroup exactly when it is maximal dissipative.
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The Lumer–Phillips theorem is a result in functional analysis, particularly within the context of operator theory. It provides conditions under which a linear operator generates a strongly continuous one-parameter semigroup (also known as a strongly continuous semigroup of operators) on a Banach space. The theorem is named after the mathematicians Fredric Lumer and William Phillips, who contributed to its development.