Near Triangularizability Implies Triangularizability
Copyright policy )Near Triangularizability Implies Triangularizability
AbstractIn this paper we consider collections of compact operators on a real or complex Banach space including linear operators on finite-dimensional vector spaces. We show that such a collection is simultaneously triangularizable if and only if it is arbitrarily close to a simultaneously triangularizable collection of compact operators. As an application of these results we obtain an invariant subspace theorem for certain bounded operators. We further prove that in finite dimensions near reducibility implies reducibility whenever the ground field isor.
- University of Toronto Canada
Invariant subspaces of linear operators, Linear transformations, semilinear transformations, reducibility, Groups and semigroups of linear operators, Quasitriangular and nonquasitriangular, quasidiagonal and nonquasidiagonal linear operators, Algebras of operators on Banach spaces and other topological linear spaces, triangularizability, invariant subspaces, linear transformations, compact operators
Invariant subspaces of linear operators, Linear transformations, semilinear transformations, reducibility, Groups and semigroups of linear operators, Quasitriangular and nonquasitriangular, quasidiagonal and nonquasidiagonal linear operators, Algebras of operators on Banach spaces and other topological linear spaces, triangularizability, invariant subspaces, linear transformations, compact operators
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