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A note on Rado's theorem

Published online by Cambridge University Press:  09 April 2009

Kong-Ming Chong
Kong-Ming Chong
Affiliation:
Department of Mathematics University of MalayaKuala Lumpur 22-11Malaysia
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Abstract

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In this note, a theorem of Rado which characterizes the convex hull of the set of all rearrangements of a given real n-tuple in terms of the Hardy—Littlewood—Pólya spectral order relation < is shown to be a consequence of a result of Hardy—Littlewood—Pólya and a strong spectral inequality.

Subject classification (Amer. Math. Soc. (MOS) 1970): 52 A 40, 52 A 20.

Information

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 26 , Issue 1 , August 1978 , pp. 86 - 88
Copyright
Copyright © Australian Mathematical Society 1978

References

Chong, K. M. (1974), “An induction principle for spectral and rearrangement inequalities”, Trans. Amer. Math. Soc. 196, 371–383.Google Scholar
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Mirsky, L. (1963), “Results and problems in the theory of doubly stochastic matrices”, Z. Wahrscheinlichkeitstheorie 1, 319–334.Google Scholar
Rado, R. (1952), “An inequality”, J. London Math. Soc. 27, 1–6.Google Scholar