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# Near Triangularizability Implies Triangularizability

Published:2004-06-01
Printed: Jun 2004
• Bamdad R. Yahaghi
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## Abstract

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 $\BR$ or $\BC$.
 Keywords: Linear transformation, Compact operator, Triangularizability, Banach space, Hilbert, space
 MSC Classifications: 47A15 - Invariant subspaces [See also 47A46] 47D03 - Groups and semigroups of linear operators {For nonlinear operators, see 47H20; see also 20M20} 20M20 - Semigroups of transformations, etc. [See also 47D03, 47H20, 54H15]

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