A remark on normal derivations |
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| Authors: | B. P. Duggal |
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| Affiliation: | Department of Mathematics and Statistics, College of Science, Sultan Qaboos University, P.O. Box 36, Al-Khod 123, Oman |
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| Abstract: | Given a Hilbert space  , let  be operators on  . Anderson has proved that if  is normal and  , then  for all operators  . Using this inequality, Du Hong-Ke has recently shown that if (instead)  , then  for all operators  . In this note we improve the Du Hong-Ke inequality to  for all operators  . Indeed, we prove the equivalence of Du Hong-Ke and Anderson inequalities, and show that the Du Hong-Ke inequality holds for unitarily invariant norms. |
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| Keywords: | Normal derivation norm inequality contraction unitarily invariant norm. |
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