Spectral order \(A\succ B\) if and only if \(A^{2p-r}\geq(A^{\frac{-r}{2}}B^pA^{\frac{-r}{2}})^{\frac{2p-r}{p-r}}\) for all \(p>r\geq 0\) and its application (Q2770419)
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scientific article; zbMATH DE number 1703256
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Spectral order \(A\succ B\) if and only if \(A^{2p-r}\geq(A^{\frac{-r}{2}}B^pA^{\frac{-r}{2}})^{\frac{2p-r}{p-r}}\) for all \(p>r\geq 0\) and its application |
scientific article; zbMATH DE number 1703256 |
Statements
5 March 2002
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bounded linear operators
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Hilbert space
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spectral order
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0.8363926
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0.82675946
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0.8100921
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0.8035596
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0.8020189
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0.7952495
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0.79462326
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Spectral order \(A\succ B\) if and only if \(A^{2p-r}\geq(A^{\frac{-r}{2}}B^pA^{\frac{-r}{2}})^{\frac{2p-r}{p-r}}\) for all \(p>r\geq 0\) and its application (English)
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Let \(A\) and \(B\) be bounded linear operators on a Hilbert space such that \(A> 0\) and \(B\geq 0\). In this paper, the author obtains a new characterization of the spectral order \(A\succ B\) as follows: \(A\succ B\) if and only if \(A^{2p- r}\geq (A^{- r/2} B^p A^{- r/2})^{{2p-r\over p-r}}\) for all real numbers \(p\) and \(r\) such that \(p> r\geq 0\). Also, an application of the above characterization is given.
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