NOTE ON THE GENERATOR OF A RAY RESOLVENT

The subject of this note is a characterization for the strong generator of a Ray resolvent. The discussion arose from the question if there exists any Hille-Yoshida type theorem in the context of Ray resolvents. More precisely the problem is the following: Given a compact space K and a linear operator L which maps a subspace Open image in new window of the space Open image in new window of continuous functions on K into Open image in new window , find necessary and sufficient conditions on (L, Open image in new window ) which ensure that L is the strong generator of a Ray resolvent on K.