Weak Limits of Consecutive Projections and of Greedy Steps

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