Geodesic
Hyperinvariant Closed Ideals for a Finitely Quasinilpotent Collection of Operators
Matematičeskie zametki, Tome 112 (2022) no. 2, pp. 269-278

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In this paper, it is proved that if $\mathscr C\ne\{0\}$ is a collection of continuous operators with modulus on an $\ell_p$-space ($1\le p\infty$) that is finitely modulus-quasinilpotent at a nonzero positive vector $x_0$ in $\ell_p$, then $\mathscr C$ and its right modulus sub-commutant $\mathscr C'_m$ have a common nontrivial invariant closed ideal.
Keywords: $\ell_p$-space, quasinilpotent operator, operator with modulus, invariant ideal, invariant subspace. 
@article{MZM_2022_112_2_a9,
     author = {Junfeng Liu},
     title = {Hyperinvariant {Closed} {Ideals} for a {Finitely} {Quasinilpotent} {Collection} of {Operators}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {269--278},
     publisher = {mathdoc},
     volume = {112},
     number = {2},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2022_112_2_a9/}
}
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Junfeng Liu. Hyperinvariant Closed Ideals for a Finitely Quasinilpotent Collection of Operators. Matematičeskie zametki, Tome 112 (2022) no. 2, pp. 269-278. http://geodesic.mathdoc.fr/item/MZM_2022_112_2_a9/