2015
DOI: 10.48550/arxiv.1511.03097
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Constructing hyper-ideals of multilinear operators between Banach spaces

Geraldo Botelho,
Ewerton R. Torres

Abstract: In view of the fact that some classical methods to construct multi-ideals fail in constructing hyper-ideals, in this paper we develop two new methods to construct hyper-ideals of multilinear operators between Banach spaces. These methods generate new classes of multilinear operators and show that some important well studied classes are Banach or p-Banach hyper-ideals.

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Cited by 1 publication
(5 citation statements)
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“…Reasoning as in the proof of [16,Theorem 3.3] with the help of the series criterion for polynomial hyper-ideals (Theorem 2.5), we get the Theorem 6.2. Let I be a p-Banach operator ideal.…”
Section: The Boundedness Methodsmentioning
confidence: 94%
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“…Reasoning as in the proof of [16,Theorem 3.3] with the help of the series criterion for polynomial hyper-ideals (Theorem 2.5), we get the Theorem 6.2. Let I be a p-Banach operator ideal.…”
Section: The Boundedness Methodsmentioning
confidence: 94%
“…Proof. We shall just check the hyper-ideal property (the remaining conditions follow the same steps of the proof of [16,Theorem 2.6]). Let P ∈ P(X ; Y)( n E; F ), Q ∈ P( m G; F ) and t ∈ L(F ; H).…”
Section: The Inequality Methodsmentioning
confidence: 99%
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