  We establish characterizations of weak input-to-state stability for abstract
dynamical systems with inputs, which are similar to characterizations of
uniform and of strong input-to-state stability established in a recent paper by
A. Mironchenko and F. Wirth. We also answer, by means of suitable
counterexamples, two open questions concerning weak input-to-state stability
(and its relation to other common stability concepts) raised in the
aforementioned paper.
