Spectral conditions on Lie and Jordan algebras of compact operators |
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Authors: | Matthew Kennedy Heydar Radjavi |
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Institution: | Department of Pure Mathematics, University of Waterloo, 200 University Ave West, Waterloo, Ontario, Canada N2L 3G1 |
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Abstract: | We investigate the properties of bounded operators which satisfy a certain spectral additivity condition, and use our results to study Lie and Jordan algebras of compact operators. We prove that these algebras have nontrivial invariant subspaces when their elements have sublinear or submultiplicative spectrum, and when they satisfy simple trace conditions. In certain cases we show that these conditions imply that the algebra is (simultaneously) triangularizable. |
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Keywords: | Invariant subspaces Spectrum Compact operators Lie algebras Jordan algebras |
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