 20110 Pavel Exner and Takashi Ichinose
 Note on a Product Formula Related to Quantum Zeno Dynamics
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Dec 30, 20

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Abstract. Given a nonnegative selfadjoint operator $H$ acting on a separable Hilbert space and an orthogonal projection $P$ such that $H_P := (H^{1/2}P)^*(H^{1/2}P)$ is densely defined, we prove that $\lim_{n
ightarrow \infty} (P\,\mathrm{e}^{itH/n}P)^n = \mathrm{e}^{itH_P}P$ holds in the strong operator topology. We also derive modifications of this product formula and its extension to the situation when $P$ is replaced by a strongly continuous projectionvalued function satisfying $P(0)=P$.
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