We prove a generalization of the Hille‐Yosida Theorem by characterizing the generators of a certain class of semigroups of unbounded operators on a Banach space. This class includes the c0‐semigroups and also a number of other classes, such as semigroups of growth order α. Our analysis shows in what sense the Cauchy Problem may be solved for the generator Z of the semigroup, and applies in particular to any unbounded densely defined operator Z on a Banach lattice with positive resolvent.
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