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Similarity of C1: Operators and the Hyperinvariant Subspace Problem

Author name : SidAhmed Ahmed M Sidha
Publication Date : 2024-04-17
Journal Name : Journal of mathematics

Abstract

In the present paper, we 0rst show that the existence of the solutions of the operator equation SXT � X is related to the similarity
of operators of class C1. , and then we give a su6cient condition for the existence of nontrivial hyperinvariant subspaces. +ese
subspaces are the closure of ran +(T) for some singular inner functions +. As an application, we prove that every C10-quasinormal
operator and C10-centered operator, under suitable conditions, have nontrivial hyperinvariant subspaces.

Keywords

Operatorsو the Hyperinvariant Subspace Problemو

Publication Link

https://doi.org/10.1155/2024/9943902

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