A weak limit theorem for sequences of parallel projections (Q2904164)

For a projection (not necessarily orthogonal) \(J\) on Hilbert space, the author of the paper under review considers the operator \(C=P-E\), where \(E\) is the orthogonal projection onto the range of \(J\) and \(P\) is the orthogonal projection onto the range of \(J^*\). The author proves that, if \(\{J_n\}\) is a sequence of projections such that the sequence \(\{C_n\}\) converges weakly to an operator \(C\), then \(C\) is not the identity operator.