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$ K$-divisibility and a theorem of Lorentz and Shimogaki


Authors: Colin Bennett and Robert Sharpley
Journal: Proc. Amer. Math. Soc. 96 (1986), 585-592
MSC: Primary 46M35; Secondary 46E30
MathSciNet review: 826485
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Abstract: The Brudnyi-Krugljak theorem on the $ K$-divisibility of Gagliardo couples is derived by elementary means from earlier results of Lorentz-Shimogaki on equimeasurable rearrangements of measurable functions. A slightly stronger form of Calderón's theorem describing the Hardy-Littlewood-Pólya relation in terms of substochastic operators (which itself generalizes the classical Hardy-Littlewood-Pólya result for substochastic matrices) is obtained.


References [Enhancements On Off] (What's this?)

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DOI: https://doi.org/10.1090/S0002-9939-1986-0826485-7
Article copyright: © Copyright 1986 American Mathematical Society