Let M, N be closed subspaces of a Hilbert space H and P, Q the orthogonal...

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Let M, N be closed subspaces of a Hilbert space H and P, Q the orthogonal projections with ran P = M, ran Q = N. Prove that the following conditions are equivalent: (b) QP = P (c) PQ = P (d) ||Px|| ||Qx|| for all x = H Let M, N be closed subspaces of a Hilbert space H and P, Q the orthogonal projections with ran P = M, ran Q = N. Prove that the following conditions are equivalent: (b) QP = P (c) PQ = P (d) ||Px|| ||Qx|| for all x = H