Relatively Bounded Extensions of Generator Perturbations

Horst R. Thieme, Jürgen Voigt
2009 Rocky Mountain Journal of Mathematics  
The Miyadera perturbation theorem provides as a by-product that operators defined on a core for the generator of a C 0 -semigroup and satisfying the Miyadera condition have a relatively bounded extension to the domain of the generator. We show that a weakening of the Miyadera condition characterizes relative boundedness with respect to the generator. We also investigate extensions of these results to Hille-Yosida operators. The various conditions we use in the abstract part are illustrated by
more » ... re illustrated by several examples. 2000 MSC: 47D06, 47D62, 47A55, 47B60
doi:10.1216/rmj-2009-39-3-947 fatcat:fhv3kbueczc55p7hedhyrm7xlm