The Friedrichs angle and alternating projections in Hilbert \(C^\ast\)-modules (Q2166413)

Let \(B\) be a \(C^*\)-algebra, \(X\) a Hilbert \(C^*\)-module over \(B\) and \(M,N\subset X\) a pair of complemented submodules. The authors prove the \(C^*\)-module version of von Neumann's alternating projections theorem and use it to show that the cosine of the Friedrichs angle \(c(M,N)\) between \(M\) and \(N\) is well-defined, and that \(c(M,N)<1\) iff \(M\cap N\) is complemented and \(M+N\) is closed.