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Spans and intersections of essentially reducing subspaces

1978
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Proceedings of the American Mathematical Society
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If P and Q are the projections onto essentially reducing subspaces M and N for an operator, the closed linear span and the intersection of M and N need not be essentially reducing or even essentially invariant. However, they are if M + N is closed, in particular if PQ = QP or if PQ is compact. 1. Introduction. If F is the orthogonal projection of separable Hilbert space 77 onto a closed subspace M, then M is invariant under a bounded linear operator T when TP -PTP = 0. It reduces F when TP -PT

doi:10.1090/s0002-9939-1978-0507334-9
fatcat:d7aycqkb35gljm6tnaobjgckha