  This paper considers composition operators on Zen spaces (a class of weighted
Bergman spaces of the right half-plane related to weighted function spaces on
the positive half-line by means of the Laplace transform). Generalizations are
given to work of Kucik on norms and essential norms, to work of Schroderus on
(essential) spectra, and to work by Arvanitidis and the authors on semigroups
of composition operators. The results are illustrated by consideration of the
Hardy--Bergman space; that is, the intersection of the Hardy and Bergman
Hilbert spaces on the half-plane.
