On Commutators of Idempotents |
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| Authors: | Heydar Radjavi Peter Rosenthal |
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| Institution: |
a Department of Mathematics, Dalhousie University, Halifax, Nova Scotia B3H 3J5, Canada.
b 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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