be two intersecting closed convex sets in a Hilbert space. Let
denote the corresponding projection operators. In 1933, von Neumann proved that the iterates produced by the sequence of alternating projections defined as
converge in norm to
are closed subspaces. L. M. Bregman
[Sov. Math., Dokl. 6, 688–692 (1965; Zbl 0142.16804
)] showed that the iterates converge weakly to a point in
for any pair of closed convex sets. In the paper under review, the author shows that alternating projections not always converge in the norm by constructing an explicit counterexample.