Аннотация:Let H
be a Hilbert space. We investigate the properties of weak limit points of iterates of random projections onto K≥2
closed convex sets in H
and the parallel properties of weak limit points of the residuals of random greedy approximation with respect to K
dictionaries. In the case of convex sets these properties imply weak convergence in all the cases known so far. In particular, we give a short proof of the theorem of Amemiya and Ando on weak convergence when the convex sets are subspaces. The question of weak convergence in general remains open.