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Commutator inequalities associated with the polar decomposition |
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| Authors: | Fuad Kittaneh |
| Institution: | Department of Mathematics, University of Jordan, Amman, Jordan |
| Abstract: | Let  be a polar decomposition of an  complex matrix  . Then for every unitarily invariant norm  , it is shown that  where  denotes the operator norm. This is a quantitative version of the well-known result that  is normal if and only if  . Related inequalities involving self-commutators are also obtained. |
| Keywords: | Commutator polar decomposition positive semidefinite matrix unitarily invariant norm |
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