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arXiv · 2509.05453

Some relationships with subnormal operators and existence of hyperinvariant subspaces

Maria F. Gamal'
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Abstract

If $T$ is a polynomially bounded operator, $\mathcal M$ is an invariant subspace of $T$, $T|_{\mathcal M}$ is a unilateral shift and $T^*|_{\mathcal M^\perp}$ 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'. 2025-09-05. Some relationships with subnormal operators and existence of hyperinvariant subspaces. https://arxiv.org/abs/2509.05453

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