A Perron theorem for the existence of invariant subspaces

DOI10.1007/BF01764120zbMath0784.47039OpenAlexW2062817484MaRDI QIDQ1191377

Giorgio Fusco, Waldyr Muniz Oliva

Publication date: 27 September 1992

Published in: Annali di Matematica Pura ed Applicata. Serie Quarta (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01764120

zbMATH Keywords

conePerron theoremexistence of invariant subspacescharacteristic values and eigenvectors of a linear operator

Mathematics Subject Classification ID

Invariant subspaces of linear operators (47A15) Linear operators on ordered spaces (47B60)

Related Items (14)

Generic behavior of flows strongly monotone with respect to high-rank cones ⋮ Generic Convergence to Periodic Orbits for Monotone Flows with Respect to 2-Cones and Applications to SEIRS Models ⋮ Monotonicity on homogeneous spaces ⋮ Convex cones associated to generalized cones in \(\mathbb R^N\) ⋮ Positivity, Monotonicity, and Consensus on Lie Groups ⋮ Transversality for cyclic negative feedback systems ⋮ Generic Poincaré-Bendixson theorem for singularly perturbed monotone systems with respect to cones of rank-2 ⋮ Semiflows “Monotone with Respect to High-Rank Cones" on a Banach Space ⋮ Transversality between invariant manifolds of periodic orbits for a class of monotone dynamical systems ⋮ Monotone dynamical systems: reflections on new advances \& applications ⋮ On random linear dynamical systems in a Banach space. I: Multiplicative ergodic theorem and Krein-Rutman type theorems ⋮ Cones of rank 2 and the Poincaré-Bendixson property for a new class of monotone systems ⋮ Existence of periodic orbits for high-dimensional autonomous systems ⋮ \(K\)-dimensional invariant cones of random dynamical systems in \(\mathbb{R}^n\) with applications

Cites Work

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• On totally positive matrices
• Transversality between invariant manifolds of periodic orbits for a class of monotone dynamical systems
• Jacobi matrices and transversality
• A dynamical systems proof of the Krein–Rutman Theorem and an extension of the Perron Theorem

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