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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Furuta's inequality and a generalization of Ando's theorem


Authors: Masatoshi Fujii and Eizaburo Kamei
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
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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).


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DOI: https://doi.org/10.1090/S0002-9939-1992-1091180-1
Article copyright: © Copyright 1992 American Mathematical Society