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Counterexample to the Trotter product formula for projections

Mate Matolcsi·Roman Shvidkoy
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Abstract

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.

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Mate Matolcsi, Roman Shvidkoy. 2001-09-07. Counterexample to the Trotter product formula for projections. https://arxiv.org/abs/math/0109049

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