On a result by Meshulam

In 1996, Meshulam proved that every sequence generated by applying projections onto affine subspaces, drawn from a finite collection in Euclidean space, must be bounded. In this paper, we extend his result not only from affine subspaces to convex polyhedral subsets, but also from Euclidean to general Hilbert space. Various examples are provided to illustrate the sharpness of the results.