Counterexample to the Trotter product formula for projections

Mate Matolcsi, Roman Shvidkoy

We constructed a unitary semigroup $(e^{tA}{)}_{t\ge 0}$ 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…