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arXiv · 2606.00865

Hyperinvariant subspaces of hyponormal operators: A constructive decomposition approach

Norberto Clemente·Eva A. Gallardo-Gutiérrez
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Abstract

It is shown that any hyponormal operator on an infinite-dimensional separable Hilbert space that admits a decomposition \( T = R + V \), where \( R \) is tridiagonal and \( V \) is trace-class, has nontrivial closed hyperinvariant subspaces provided $T$ is not a multiple of the identity. We further discuss implications of this result for the invariant subspace problem of hyponormal operators answering, in particular, negatively to a question raised by Kim and Lee \cite{kimlee} regarding an explicit approach to such a problem. Finally, we characterize the existence of reducing subspaces for hyponormal operators addressing an approach by Aronszajn and Smith.

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Norberto Clemente, Eva A. Gallardo-Gutiérrez. 2026-05-30. Hyperinvariant subspaces of hyponormal operators: A constructive decomposition approach. https://doi.org/10.1112/blms.70399

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