Invariant subspaces for non-normable Fréchet spaces
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DOI: 10.1016/j.aim.2018.09.039
Abstract: A Fr\'echet space $X$ satisfies the Hereditary Invariant Subspace (resp. Subset) Property if for every closed infinite-dimensional subspace $M$ in $X$, each continuous operator on $M$ possesses a non-trivial invariant subspace (resp. subset). In this… read more here.
Keywords: non trivial; non normable; subspace; continuous operator ... See more keywords
The invariant subspace problem for non-Archimedean Köthe spaces
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DOI: 10.1016/j.jmaa.2017.04.034
Abstract: Abstract In this study, a proof is given that if a non-Archimedean Kothe space Λ, which is generated by an infinite matrix B = ( b n k ) k , n ∈ N such… read more here.
Keywords: subspace problem; non archimedean; archimedean spaces; invariant subspace ... See more keywords
On quasinilpotent operators and the invariant subspace problem
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DOI: 10.1016/j.jmaa.2019.04.026
Abstract: We show that a bounded quasinilpotent operator $T$ acting on an infinite dimensional Banach space has an invariant subspace if and only if there exists a rank one operator $F$ and a scalar $\alpha\in\mathbb{C}$, $\alpha\neq… read more here.
Keywords: quasinilpotent operators; operators invariant; quasinilpotent; invariant subspace ... See more keywords