In the Amemiya-Ando problem 3 is enough

preprint2012arXivOpen access

In any infinite dimensional Hilbert space $\mathcal H$ there exist orthogonal projections $Q_1$ , $Q_2$ and $Q_3$ , such that a sequence $(P_n... P_1(x))$ diverges in norm for some $P_1,P_2,...\in\{Q_1,Q_2,Q_3\}$ and $x\in\mathcal H$ .

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In the Amemiya-Ando problem 3 is enough

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