Ritt operators and convergence in the method of alternating projections (Q259103)

Let \(M_1,\ldots,M_N\) be subspaces of a Hilbert space \(X\) and let \(P_1,\ldots,P_N\) be the corresponding orthogonal projections. Denote by \(M\) the intersection \(M_1\cap\cdots\cap M_N\) and by \(P_M\) the orthogonal projection onto \(M\). For a vector \(x\) in \(X\), the sequence of vectors \(\{x_n\}_{n\geq0}\) is defined by NEWLINE\[NEWLINE x_0=x,\quad x_{n+1}=P_N\cdots P_1x_n,~n\geq0. NEWLINE\]NEWLINE It is well known that the sequence \(\{x_n\}_{n\geq0}\) converges in the norm to \(P_Mx\). The authors of the paper under review study the rate of this convergence. To obtain their results, they use properties of Ritt operators.