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October 3, 2025Open Access

Some relationships with subnormal operators and existence of hyperinvariant subspaces

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Authors

MGMaria F. Gamal'

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Overview

Analysis reveals that polynomially bounded operators can exhibit hyperinvariant subspaces, suggesting new pathways in operator theory.

Key Points

  • If a polynomially bounded operator has a specific invariant subspace, then it possesses a nontrivial hyperinvariant subspace.
  • The operators involved must include both a unilateral shift and a subnormal operator in orthogonal complement for this outcome.
  • Intertwining a polynomially bounded operator with hyponormal and its adjoint also ensures the existence of a nontrivial hyperinvariant subspace.
  • The direct study of hyperinvariant subspaces specific to subnormal operators is not the focus here.

Cite This Study

Maria F. Gamal' (2025) studied this question.

synapsesocial.com/papers/68e034f7f0e39f13e7fa3008https://doi.org/10.48550/arxiv.2509.05453
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