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Spans and intersections of essentially reducing subspaces


Author: Michael J. Hoffman
Journal: Proc. Amer. Math. Soc. 72 (1978), 333-340
MSC: Primary 47A15
DOI: https://doi.org/10.1090/S0002-9939-1978-0507334-9
MathSciNet review: 507334
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Abstract: 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.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1978-0507334-9
Keywords: Essentially invariant subspaces, essentially reducing subspaces, compact perturbations, Calkin algebra
Article copyright: © Copyright 1978 American Mathematical Society

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