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arXiv · 1508.05029

Strange products of projections

Eva Kopecká·Adam Paszkiewicz
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Abstract

Let $H$ be an infinite dimensional Hilbert space. We show that there exist three orthogonal projections $X_1, X_2, X_3$ onto closed subspaces of $H$ such that for every $0\ne z_0\in H$ there exist $k_1, k_2,\dots \in \{1,2,3\}$ so that the sequence of iterates defined by $z_n= X_{k_n} z_{n-1}$ does not converge in norm.

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Eva Kopecká, Adam Paszkiewicz. 2015-08-20. Strange products of projections. https://arxiv.org/abs/1508.05029

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