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Proceedings of the American Mathematical Society

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

 
 

 

Inequalities for the powers of nonnegative Hermitian operators


Author: Man Kam Kwong
Journal: Proc. Amer. Math. Soc. 51 (1975), 401-406
MSC: Primary 47B15
DOI: https://doi.org/10.1090/S0002-9939-1975-0374970-X
MathSciNet review: 0374970
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Abstract: In the set of bounded Hermitian operators from a Hilbert space $ H$ into itself, we define three types of ordering by means of the cones of nonnegative, positive definite and positive invertible operators respectively. Our main theorem shows that for all three types of ordering, if $ A$ is ``greater'' than $ B$, then $ {A^r}$ is ``greater'' than $ {B^r}$ for all real numbers $ r \leq 1$. This generalizes the results of Heinz [3] and Kato [4].


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DOI: https://doi.org/10.1090/S0002-9939-1975-0374970-X
Article copyright: © Copyright 1975 American Mathematical Society

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