Furuta’s inequality and a generalization of Ando’s theorem
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- by Masatoshi Fujii and Eizaburo Kamei PDF
- Proc. Amer. Math. Soc. 115 (1992), 409-413 Request permission
Abstract:
As a continuation of our preceding notes, we discuss Furuta’s inequality under the chaotic order defined by $\log A \geq \log B$ for positive invertible operators $A$ and $B$. We prove that Furuta’s type inequalities ${\left ( {{B^r}{A^p}{B^r}} \right )^{2r/\left ( {p + 2r} \right )}} \geq {B^{2r}}$ and ${A^{2r}} \geq {\left ( {{A^r}{B^p}{A^r}} \right )^{2r/\left ( {p + 2r} \right )}}$ hold true for $p \geq r \geq 0$, which is a generalization of an inequality due to Ando (Math. Ann. 279 (1987), 157-159).References
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Additional Information
- © Copyright 1992 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 115 (1992), 409-413
- MSC: Primary 47A63; Secondary 47B15
- DOI: https://doi.org/10.1090/S0002-9939-1992-1091180-1
- MathSciNet review: 1091180