| Young's Inequality for Positive Operators |
| Received:April 24, 2010 Revised:October 11, 2010 |
| Key Words:
Young's inequality positive operator.
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| Fund Project:Supported by the National Natural Science Foundation of China (Grant Nos.10871224;11026134) and the Special Research Project of Educational Department of Shaanxi Province (Grant No.09JK741). |
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| Abstract: |
| The classical Young's inequality and its refinements are applied to positive operators on a Hilbert space at first. Based on the classical Poisson integral formula of relevant operators, some new inequalities on unitarily invariant norm of $A^\frac1pXB^\frac1q-A^\frac1qYB^\frac1p$ are obtained with effective calculation, where $A$, $B$, $X$, $Y\in{\cal B}({\cal H})$ with $A$, $B\geqslant 0$ and $1 |
| Citation: |
| DOI:10.3770/j.issn:1000-341X.2011.05.018 |
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