Spans and intersections of essentially reducing subspaces

Hoffman, Michael J.

doi:10.1090/S0002-9939-1978-0507334-9

Spans and intersections of essentially reducing subspaces
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by Michael J. Hoffman

Proc. Amer. Math. Soc. 72 (1978), 333-340

DOI: https://doi.org/10.1090/S0002-9939-1978-0507334-9

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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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