Operator equations and invariant subspaces
Keywords:
Invariant subspaces, Hyperinvariant subspacesAbstract
Banach space operators acting on some fixed space X are considered. If two such operators A and B verify the condition A2=B2 and if A has nontrivial hyperinvariant subspaces, then B has nontrivial invariant subspaces. If A and B commute and satisfy a special type of functional equation, and if A is not a scalar multiple of the identity, the author proves that if A has nontrivial invariant subspaces, then so does B.
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