Similarity of C1: Operators and the Hyperinvariant Subspace Problem

Abdelkader Segres, Ahmed Bachir, Sid Ahmed Ould Ahmed Mahmoud and G. Muhiuddin

Journal of Mathematics, 2024, vol. 2024, 1-9

Abstract: In the present paper, we first show that the existence of the solutions of the operator equation S∗XT=X is related to the similarity of operators of class C1., and then we give a sufficient condition for the existence of nontrivial hyperinvariant subspaces. These subspaces are the closure of ranφT for some singular inner functions φ. As an application, we prove that every C10-quasinormal operator and C10-centered operator, under suitable conditions, have nontrivial hyperinvariant subspaces.

Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:9943902

DOI: 10.1155/2024/9943902

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