Abstract
We prove the existence of a non-trivial hyperinvariant subspace for several sets of polynomially compact operators. The main results of the paper are: (i) a non-trivial norm closed algebra \(\mathcal {A}\subseteq \mathcal {B}(\mathscr {X})\) which consists of polynomially compact quasinilpotent operators has a non-trivial hyperinvariant subspace; (ii) if there exists a non-zero compact operator in the norm closure of the algebra generated by an operator band \(\mathcal {S}\), then \(\mathcal {S}\) has a non-trivial hyperinvariant subspace.
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Acknowledgements
The authors would like to thank the anonymous referee for carefully reading the manuscript. The paper is a part of the project Distinguished subspaces of a linear operator and the work of the first author was partially supported by the Slovenian Research Agency through the research program P2-0268. The second author acknowledges financial support from the Slovenian Research Agency, Grants Nos. P1-0222, J1-2453 and J1-2454.
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Communicated by Mostafa Mbekhta.
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Bračič, J., Kandić, M. Hyperinvariant subspaces for sets of polynomially compact operators. Ann. Funct. Anal. 13, 71 (2022). https://doi.org/10.1007/s43034-022-00214-4
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DOI: https://doi.org/10.1007/s43034-022-00214-4