Approximate observability of abstract evolution equation with unbounded observation operator

Properties of the null set of the evolution equation ẋ = Ax(t), x(0) = xo, y(t) = Cx(t) (A generates a strongly continuous semigroup {S(t)}t≥o on a Banach space X, C is a linear unbounded operator) are investigated. Conditions for approximate observability of such system are obtained.