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Similarity of C1: Operators and the Hyperinvariant Subspace Problem

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  • Abdelkader Segres
  • Ahmed Bachir
  • Sid Ahmed Ould Ahmed Mahmoud
  • G. Muhiuddin

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.

Suggested Citation

  • Abdelkader Segres & Ahmed Bachir & Sid Ahmed Ould Ahmed Mahmoud & G. Muhiuddin, 2024. "Similarity of C1: Operators and the Hyperinvariant Subspace Problem," Journal of Mathematics, Hindawi, vol. 2024, pages 1-9, April.
    • Handle: RePEc:hin:jjmath:9943902
    DOI: 10.1155/2024/9943902
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