This is an announcement for the paper "The closedness of the generator of a semigroup" by George Androulakis and Matthew Ziemke.

Abstract: We study semigroups of bounded operators on a Banach space such that the members of the semigroup are continuous with respect to various weak topologies and we give sufficient conditions for the generator of the semigroup to be closed with respect to the topologies involved. The proofs of these results use the Laplace transforms of the semigroup. Thus we first give sufficient conditions for Pettis integrability of vector valued functions with respect to scalar measures.

Archive classification: math.FA math-ph math.MP

Submitted from: giorgis@math.sc.edu

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1503.07472

or

http://arXiv.org/abs/1503.07472