Invariant subspaces of nilpotent linear operators, I [PDF]
Journal für die reine und angewandte Mathematik (Crelles Journal), 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 $T$.
Ringel, Claus Michael +1 more
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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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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
doaj +1 more source
Symmetric invariant subspaces of complexifications of linear operators [PDF]
Mathematical Notes, 2012 3 ...
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A study on the unicellularity of some lower triangular operators [PDF]
, 1994 The investigation of invariant subspaces is the first step in the attempt to understand the structure of operators. We will investigate bounded linear operators on Hilbert spaces which have the simplest possible invariant subspace structure. ..
Baik Hyoung Gu, Kang Joo Ho
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Hamiltonians with Riesz Bases of Generalised Eigenvectors and Riccati Equations [PDF]
, 2010 An algebraic Riccati equation for linear operators is studied, which arises in systems theory. For the case that all involved operators are unbounded, the existence of infinitely many selfadjoint solutions is shown. To this end, invariant graph subspaces
Wyss, Christian
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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.
Kasjan, Stanisław, Kosakowska, Justyna
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Invariant Subspaces of Collectively Compact Sets of Linear Operators
Positivity, 2008 The authors introduce some invariant subspace results for collectively compact families of operators and they also show that any collectively compact set of operators satisfies the Berger--Wang formula [\textit{M.\,A.\thinspace Berger} and \textit{Y.\,Wang}, Linear Algebra Appl.\ 166, 21--27 (1992; Zbl 0818.15006)] in a special case.
Mısırlıoğlu, Remzi Tunç +1 more
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Invariant subspaces for algebras of linear operators and amenable locally compact groups [PDF]
Proceedings of the American Mathematical Society, 1988 Let G G be a locally compact group. We prove in this paper that G G is amenable if and only if the group algebra L 1 ( G ) {L_1}\left ( G \right ) (respectively the measure algebra M
Lau, Anthony To-Ming, Wong, James C. S.
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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 $ $, denote by $N_ $ the nilpotent linear operator of Jordan type $ $. Given partitions $ $, $ $, we investigate the representation space ${}_2{\mathbb V}_ ^ $ of all short exact sequences $$ \mathcal E: 0\to N_ \to N_ \to N_ \to 0$$ where $ $ is any partition with each part at most 2.
Kaniecki, Mariusz +2 more
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