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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)


Two operator functions with monotone property

Author: Takayuki Furuta
Journal: Proc. Amer. Math. Soc. 111 (1991), 511-516
MSC: Primary 47A60; Secondary 47B15
MathSciNet review: 1045135
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Abstract: This paper proves that $ F(p) = {({B^r}{A^p}{B^r})^{(1 + 2r)/(p + 2r)}}$ is an increasing function of $ p$ for $ p \geqq 1$ and $ r \geqq 0$ whenever $ A \geqq B \geqq 0$. This result is more precise than our previous result that $ A \geqq B \geqq 0$ ensures $ {({B^r}{A^p}{B^r})^{(1 + 2r)/(p + 2r)}} \geqq {B^{1 + 2r}}$ for each $ p \geqq 1$ and $ r \geqq 0$. We also cite three counterexamples related to Theorem 1.

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Additional Information

PII: S 0002-9939(1991)1045135-2
Keywords: Positive operator, order-preserving inequalities
Article copyright: © Copyright 1991 American Mathematical Society

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