  We constructed a unitary semigroup $(e^{tA})_{t \geq 0}$ on a Hilbert space
and an orthogonal projection $P$ such that the limit $\lim_{n \to \infty} [
e^{\frac{t}{n}A}P ]^n$ does not exist strongly. A similar example with a
positive contractive semigroup and positive contractive projection on $L_p$ is
also constructed.
