Numerical Radius and Operator Norm Inequalities
A general inequality involving powers of the numerical radius for sums and products of Hilbert space operators is given. This inequality generalizes several recent inequalities for the numerical radius, and includes that if A and B are operators on a complex Hilbert space H, then wr(A∗B)&...
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| Format: | Article |
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2009-01-01
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| Series: | Journal of Inequalities and Applications |
| Online Access: | http://dx.doi.org/10.1155/2009/492154 |
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doaj-e2ce6581c6664f9097872925636fadee2020-11-24T20:54:29ZengSpringerOpenJournal of Inequalities and Applications1025-58341029-242X2009-01-01200910.1155/2009/492154Numerical Radius and Operator Norm InequalitiesKhalid ShebrawiHussien AlbadawiA general inequality involving powers of the numerical radius for sums and products of Hilbert space operators is given. This inequality generalizes several recent inequalities for the numerical radius, and includes that if A and B are operators on a complex Hilbert space H, then wr(A∗B)≤(1/2)‖|A|2r+|B|2r‖ for r≥1. It is also shown that if Xi is normal (i=1,2,…,n), then ‖∑i=1nXi‖r≤nr−1‖∑i=1n|Xi|r‖. Related numerical radius and usual operator norm inequalities for sums and products of operators are also presented. http://dx.doi.org/10.1155/2009/492154 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Khalid Shebrawi Hussien Albadawi |
| spellingShingle |
Khalid Shebrawi Hussien Albadawi Numerical Radius and Operator Norm Inequalities Journal of Inequalities and Applications |
| author_facet |
Khalid Shebrawi Hussien Albadawi |
| author_sort |
Khalid Shebrawi |
| title |
Numerical Radius and Operator Norm Inequalities |
| title_short |
Numerical Radius and Operator Norm Inequalities |
| title_full |
Numerical Radius and Operator Norm Inequalities |
| title_fullStr |
Numerical Radius and Operator Norm Inequalities |
| title_full_unstemmed |
Numerical Radius and Operator Norm Inequalities |
| title_sort |
numerical radius and operator norm inequalities |
| publisher |
SpringerOpen |
| series |
Journal of Inequalities and Applications |
| issn |
1025-5834 1029-242X |
| publishDate |
2009-01-01 |
| description |
A general inequality involving powers of the numerical radius for sums and products of Hilbert space operators is given. This inequality generalizes several recent inequalities for the numerical radius, and includes that if A and B are operators on a complex Hilbert space H, then wr(A∗B)≤(1/2)‖|A|2r+|B|2r‖ for r≥1. It is also shown that if Xi is normal (i=1,2,…,n), then ‖∑i=1nXi‖r≤nr−1‖∑i=1n|Xi|r‖. Related numerical radius and usual operator norm inequalities for sums and products of operators are also presented. |
| url |
http://dx.doi.org/10.1155/2009/492154 |
| work_keys_str_mv |
AT khalidshebrawi numericalradiusandoperatornorminequalities AT hussienalbadawi numericalradiusandoperatornorminequalities |
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