\(A\geqq B\geqq 0\) ensures \((A^{\frac{r}{2}}A^pA^{\frac{r}{2}})^{\frac{1}{q}}\geqq (A^{\frac{r}{2}}B^pA^{\frac{r}{2}})^{\frac{1}{q}}\) for \(p\geqq 0\), \(q\geqq 1\), \(r\geqq 0\) with \((1+r)q\geqq p+r\) and its applications (Q2747297)
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 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: \(A\geqq B\geqq 0\) ensures \((A^{\frac{r}{2}}A^pA^{\frac{r}{2}})^{\frac{1}{q}}\geqq (A^{\frac{r}{2}}B^pA^{\frac{r}{2}})^{\frac{1}{q}}\) for \(p\geqq 0\), \(q\geqq 1\), \(r\geqq 0\) with \((1+r)q\geqq p+r\) and its applications |
scientific article; zbMATH DE number 1657484
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | \(A\geqq B\geqq 0\) ensures \((A^{\frac{r}{2}}A^pA^{\frac{r}{2}})^{\frac{1}{q}}\geqq (A^{\frac{r}{2}}B^pA^{\frac{r}{2}})^{\frac{1}{q}}\) for \(p\geqq 0\), \(q\geqq 1\), \(r\geqq 0\) with \((1+r)q\geqq p+r\) and its applications |
scientific article; zbMATH DE number 1657484 |
Statements
18 June 2002
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Löwner-Heinz inequality
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Furuta inequality
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0.9719691
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0.9354119
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0.9182078
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0.90433264
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0.8578557
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0.83488613
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0.8299569
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\(A\geqq B\geqq 0\) ensures \((A^{\frac{r}{2}}A^pA^{\frac{r}{2}})^{\frac{1}{q}}\geqq (A^{\frac{r}{2}}B^pA^{\frac{r}{2}})^{\frac{1}{q}}\) for \(p\geqq 0\), \(q\geqq 1\), \(r\geqq 0\) with \((1+r)q\geqq p+r\) and its applications (English)
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Given bounded linear operators \(A\) , \(B\) on a Hilbert space \(\mathcal H\) , denote \(A \geq 0\) if \((A x , x)\geq 0\) for all \(x \in \mathcal H \), and denote \(A \geq B\) if \(A - B \geq 0\). The paper surveys several applications of the inequality made in its title (Furuta ineqality)to some operator and norm inequalities , to operator equations. The bibliography contains more then 80 titles.
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