On Commutators of Idempotents |
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| Authors: | Heydar Radjavi Peter Rosenthal |
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| Institution: | 1. Department of Mathematics , Dalhousie University , Halifax, Nova Scotia, B3H 3J5, Canada;2. Department of Mathematics , University of Toronto , Toronto, Ontario, M5S 3G3, Canada |
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| Abstract: | It is shown that a pair of idempotent operators on a Banach space is triangularizable if their commutator is nilpotent. Moreover, if every operator on Hilbert space has an invariant subspace, then a pair of idempotents on Hilbert space is triangularizable if their commutator is quasinilpotent. These results are generalized from idempotents to quadratic operators. |
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| Keywords: | Banach Space Hilbert Space Idempotent |
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