Results 1 to 10 of about 166,152,496 (189)
Invariant subspaces of nilpotent linear operators, I [PDF]
Journal Fur Die Reine Und Angewandte Mathematik, 2008 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 $V$, and $U$ is an invariant subspace with respect to $T$.
Claus Michael Ringel +1 more
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Symmetric invariant subspaces of complexifications of linear operators [PDF]
Mathematical Notes, 2012 3 ...
K V Storozhuk
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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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Discrete and Continuous Dynamical Systems, 2007 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. By means of the useful concept of deficiency, we can write explicit basis for these spaces of differential operators.
Robert Milson +2 more
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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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Operations on arc diagrams and degenerations for invariant subspaces of linear operators [PDF]
Transactions of the American Mathematical Society, 2014 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. Moreover, a combinatorial characterization of the partial order given by degenerations is described.
Kosakowska, Justyna, Schmidmeier, Markus
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A swiss cheese theorem for linear operators with two invariant subspaces [PDF]
Proceedings of the American Mathematical Society, 2015 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 $U_1\subset U_2\subset V$. Let $\mathcal S(n)$ be the category of such systems where the operator $T$ acts with nilpotency index at most $n$.
Moore, Audrey, Schmidmeier, Markus
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Lomonosov’s invariant subspace theorem for multivalued linear operators [PDF]
Proceedings of the American Mathematical Society, 2002 The famous Lomonosov’s invariant subspace theorem states that if a continuous linear operator T T on an
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Operations on arc diagrams and degenerations for invariant subspaces of linear operators. Part II [PDF]
Communications in Algebra, 2017 For a partition $β$, denote by $N_β$ the nilpotent linear operator of Jordan type $β$. Given partitions $β$, $γ$, we investigate the representation space ${}_2{\mathbb V}_γ^β$ of all short exact sequences $$ \mathcal E: 0\to N_α\to N_β\to N_γ\to 0$$ where $α$ is any partition with each part at most 2.
Kaniecki, Mariusz +2 more
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