An invariant subspace problem for multilinear operators on finite dimensional spaces
Słowa kluczowe
Invariant subspaces, multilinear operators, polynomial operators, topological degree, admissible operatorsAbstrakt
We introduce the notion of invariant subspaces for multilinear operators from which the invariant subspace problems for multilinear and polynomial operators arise. We prove that polynomial operators acting in a finite dimensional complex space and even polynomial operators acting in a finite dimensional real space have eigenvalues. These results enable us to prove that polynomial and multilinear operators acting in a finite dimensional complex space, even polynomial and even multilinear operators acting in a finite dimensional real space have nontrivial invariant subspaces. Furthermore, we prove that odd polynomial operators acting in a finite dimensional real space either have eigenvalues or are homotopic to scalar operators; we then use this result to prove that odd polynomial and odd multilinear operators acting in a finite dimensional real space may or may not have invariant subspaces.Pobrania
Opublikowane
2016-04-12
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1.
EMENYU, John. An invariant subspace problem for multilinear operators on finite dimensional spaces. Topological Methods in Nonlinear Analysis [online]. 12 kwiecień 2016, T. 44, nr 1, s. 1–10. [udostępniono 22.7.2024].
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