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Analysis reveals that polynomially bounded operators can exhibit hyperinvariant subspaces, suggesting new pathways in operator theory.
If T is a polynomially bounded operator, M is an invariant subspace of T, T|M is a unilateral shift and T^*|M^⊥ is subnormal, then T has a nontrivial hyperinvariant subspace. If an operator T is intertwined from both sides with two operators, one of which is hyponormal and other is the adjoint to hyponormal, then T has a nontrivial hyperinvariant subspace. The existence of nontrivial hyperinvariant subspaces for subnormal operators themselves is not studied here.
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Maria F. Gamal' (2025) studied this question.
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