On semigroups with an infinitesimal operator
Volume 85 / 2005
Annales Polonici Mathematici 85 (2005), 77-89
MSC: 54C60, 54C65, 39B12.
DOI: 10.4064/ap85-1-6
Abstract
Let $\{F^{t}:t\geq 0\}$ be an iteration semigroup of linear continuous set-valued functions. If the semigroup has an infinitesimal operator then it is a uniformly continuous semigroup majorized by an exponential semigroup. Moreover, for sufficiently small $t$ every linear selection of $F^{t}$ is invertible and there exists an exponential semigroup $\{f^{t}:t\geq 0\}$ of linear continuous selections $f^{t}$ of $F^{t}$.
