Errata Corrige: ''Two extensions of the alternating algorithm of von Neumann'' (Q800588)

In Theorems 1 and 2 the assumption that \(U+V\) is a linear subspace cannot be omitted. In fact, the given proof relies on the fact that \(J_{2n}(w- w_ n)\leq\sigma_ n(\sigma_ n\to 0)\) which does not follow from the established inequalities \(J_{2n}(w)\leq\epsilon_ n\), \(J_{2n}(w_ n)\leq\epsilon_ n (\epsilon_ n\to 0)\). However, if \(U+V\) is a linear subspace, since \((w-w_ n)\in U+V\) it can be shown that \(J_{2n}(w-w_ n)\leq\epsilon_ n\) the same way that it was for \(J_{2n}(w)\) or \(J_{2n}(w_ n)\). It is a very regrettable fact that Lemma 5 ii) and Theorem 3 respectively have an incorrect proof and no proof at all so that Theorem 4 need not be true.