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Strange products of projections

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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 ≠ z 0 ∈ H there exist k 1, k 2, · · · ∈ {1, 2, 3} so that the sequence of iterates defined by z n = X kn z n −1 does not converge in norm.

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Authors and Affiliations

  1. Department of Mathematics, University of Innsbruck, A-6020, Innsbruck, Austria

    Eva Kopecká

  2. Faculty of Mathematics and Computer Science, Łódź University, Banacha 22, 90-238, Łódź, Poland

    Adam Paszkiewicz

Authors
  1. Eva Kopecká
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  2. Adam Paszkiewicz
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Correspondence to Eva Kopecká.

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Kopecká, E., Paszkiewicz, A. Strange products of projections. Isr. J. Math. 219, 271–286 (2017). https://doi.org/10.1007/s11856-017-1480-4

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  • DOI: https://doi.org/10.1007/s11856-017-1480-4

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