Unified Grothendieck’s and Kwapień’s Theorems for Multilinear Operators

arxiv(2024)

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摘要
Kwapień’s theorem asserts that every continuous linear operator from ℓ _1 to ℓ _p is absolutely ( r,1) -summing for 1/r=1-| 1/p-1/2| . When p=2 it recovers the famous Grothendieck’s theorem. In this paper we investigate multilinear variants of these theorems and related issues. Among other results we present a unified version of Kwapień’s and Grothendieck’s results that encompasses the cases of multiple summing and absolutely summing multilinear operators.
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关键词
Grothendieck’s theorem,Kwapień’s theorem,Multilinear operators,Sequence spaces
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