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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.

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
Hardy, G. H., Littlewood, J. E. and Pólya, G. (1934), Inequalities (Cambridge University Press, New York).Google Scholar
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