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- W2899449301 abstract "Let n be a natural number, Λ⊆Nn such that 1,…,1∈Λ. As a simultaneous extension of the p-summing and multiple p-summing operators we introduce the class of all n-linear operators which are p,Λ-summing, 1≤p<∞. If 1≤p≤q≤∞, 1≤r≤∞ are such that 1/p=(1/q)+(1/r) we introduce the class MPSq,pΛ of the operators with the Maurey–Pietsch q,p,Λ-splitting property as the multilinear analogue of the class of q,p-mixing linear operators and, as particular classes, MPSq,p, MPSq,pmult. We introduce two new classes of multilinear operators both being the multilinear analogues of the class of r-nuclear operators, namely, the class of r-nuclear operators with respect to the πpΛ-norm, NrπpΛ and the class Pr,pΛ and prove that Nr⊂NrπpΛ⊂Pr,pΛ⊂MPSq,pΛ. By concrete examples, we show that, contrary to the linear case, when Πr⊂Mq,p, in the multilinear case the inclusions Π2mult⊂MP2,1mult, Δ2⊂MP2,1mult are not true, which is in contrast to a well-known result shown by us in another paper that Δ2⊂MP2,1." @default.
- W2899449301 created "2018-11-09" @default.
- W2899449301 creator A5032304230 @default.
- W2899449301 date "2018-10-30" @default.
- W2899449301 modified "2023-10-17" @default.
- W2899449301 title "Operators with the Maurey–Pietsch multiple splitting property" @default.
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- W2899449301 doi "https://doi.org/10.1080/03081087.2018.1536733" @default.
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