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Near Triangularizability Implies Triangularizability
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- Journal:
- Canadian Mathematical Bulletin / Volume 47 / Issue 2 / 01 June 2004
- Published online by Cambridge University Press:
- 20 November 2018, pp. 298-313
- Print publication:
- 01 June 2004
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- Article
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In 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 is
$\mathbb{R}$ or 
$\mathbb{C}$.
