Invariant Subspaces of Nilpotent Linear Operators. I [PDF]
Journal für die reine und angewandte Mathematik (Crelles Journal), 2006 Let $k$ be a field. We consider triples $(V,U,T)$, where $V$ is a finite dimensional $k$-space, $U$ a subspace of $V$ and $T \:V \to V$ a linear operator with $T^n = 0$ for some $n$, and such that $T(U) \subseteq U$. Thus, $T$ is a nilpotent operator on $
Bourbaki N. +3 more
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Operations on Arc Diagrams and Degenerations for Invariant Subspaces of Linear Operators [PDF]
Transactions of the American Mathematical Society, 2013 We study geometric properties of varieties associated with invariant subspaces of nilpotent operators. There are reductive algebraic groups acting on these varieties. We give dimensions of orbits of these actions.
Kosakowska, Justyna, Schmidmeier, Markus
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The Swiss Cheese Theorem for Linear Operators with Two Invariant Subspaces [PDF]
Proceedings of the American Mathematical Society, 2014 We study systems $(V,T,U_1,U_2)$ consisting of a finite dimensional vector space $V$, a nilpotent $k$-linear operator $T:V\to V$ and two $T$-invariant subspaces $U_1\subset U_2\subset V$.
Moore, Audrey, Schmidmeier, Markus
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Symmetric invariant subspaces of complexifications of linear operators [PDF]
Mathematical Notes, 2012 3 ...
K V Storozhuk
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Structure theorems for linear and non-linear differential operators admitting invariant polynomial subspaces [PDF]
Discrete and Continuous Dynamical Systems, 2006 In this paper we derive structure theorems that characterize the spaces of linear and non-linear differential operators that preserve finite dimensional subspaces generated by polynomials in one or several variables.
Gomez-Ullate, David +2 more
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Invariant Subspaces for a Semigroup of Linear Operators
Proceedings of the Koninklijke Nederlandse Akademie Van Wetenschappen Series A, Indagationes Mathematicae, 1965 Following result is shown using similar arguments to those in the author's previous work [Isr. J. Math. 2, 19--26 (1964; Zbl 0131.33101)]. Let \(E\) be a locally convex Hausdorff space, and \(H\) a closed subspace in \(E\) of finite codimension \(n\). Let \(X\) be a set in \(E\) having the following properties: (1) \(X \cap (x + H)\) is compact convex ...
Ky Fan
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Weighted Hardy spaces: shift invariant and coinvariant subspaces, linear systems and operator model theory [PDF]
Acta Scientiarum Mathematicarum, 2013 The Sz.-Nagy--Foias model theory for $C_{\cdot 0}$ contraction operators combined with the Beurling-Lax theorem establishes a correspondence between any two of four kinds of objects: shift-invariant subspaces, operator-valued inner functions ...
Ball, Joseph A., Bolotnikov, Vladimir
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The existence of Hall polynomials for x2-bounded invariant subspaces of nilpotent linear operators
Journal of Pure and Applied Algebra, 2022 We prove the existence of Hall polynomials for $x^2$-bounded invariant subspaces of nilpotent linear operators.
Stanisław Kasjan, Justyna Kosakowska
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Degenerate Multi-Term Equations with Gerasimov–Caputo Derivatives in the Sectorial Case
Mathematics, 2022 The unique solvability for the Cauchy problem in a class of degenerate multi-term linear equations with Gerasimov–Caputo derivatives in a Banach space is investigated.
Vladimir E. Fedorov, Kseniya V. Boyko
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Approximately invariant subspaces for unbounded linear operators. II
Mathematische Annalen, 1977 Palle E T Jørgensen
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