April 5, 2024Open Access

On existence of hyperinvariant subspaces for quasinilpotent operators with a nonsymmetry in the growth of the resolvent

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Abstract

Let T be a quasinilpotent operator on a Banach space. Under assumptions of a certain nonsymmetry in the growth of the resolvent of T, it is proved that every operator in the commutant of T is not unicellular. In particular, T has nontrivial hyperinvariant subspaces. The proof is based on a modification of the reasoning of S.

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Maria F. Gamal' (Fri,) studied this question.

synapsesocial.com/papers/68e70547b6db64358767f290 https://doi.org/https://doi.org/10.48550/arxiv.2404.04348

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