Symmetric ideals of generalized summing multilinear operators

Botelho, Geraldo; Santiago, Ariel S.

doi:10.1080/03081087.2023.2300668

Cited by 2 publications

(4 citation statements)

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“…In Section 4 we give two applications of ideal-representability that are not related to ideal-representability at first glance. Namely, we improve an important result from [22] and a very recent result from [10].…”

Section: Introductionsupporting

confidence: 55%

“…In this section we give a few more applications of our study on ideal-representable sequence classes, namely, we generalize results from [22] and [10].…”

Section: Further Applicationsmentioning

confidence: 97%

“…Section 2). This approach has proved to be quite fruitful, see, e.g., [1,2,7,9,10,11,12,25,27,28]. The usefulness of the examples described above for the classes ℓ w p , ℓ u p , ℓ p • and ℓ 1 (•) make the following question quite natural: Given a sequence class X, are there a scalar-valued sequence space λ and a Banach operator ideal I such that the correspondence…”

Section: Introductionmentioning

confidence: 99%

“…it is natural to wonder if every linearly stable sequence class X such that X(K) = ℓ p lies between ℓ p • and ℓ w p . In [10,Proposition 6.3] we gave a partial solution for p > 1 and X enjoying certain properties. Now, with the theory of ideal-representable sequence classes, we are in the position to give a complete positive solution to the problem.…”

mentioning

confidence: 99%

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Hyper-ideals of Multilinear Operators and Two-Sided Polynomial Ideals Generated by Sequence Classes

Botelho

Wood

2022

Mediterr. J. Math.

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It is well known that weakly p-summable sequences in a Banach space E are associated to bounded operators from ℓ p * to E, and unconditionally p-summable sequences in E are associated to compact operators from ℓ p * to E. Generalizing these results to a quite wide environment, we characterize the classes of Banach spaces-valued sequences that are associated to (or represented by) some Banach operator ideal. Using these characterizations, we decide, among all sequence classes that usually appear in the literature, which are represented by some Banach operator ideal and which are not. Moreover, to each class that is represented by some Banach operator ideal, we show an ideal that represents it. Illustrative examples and additional applications are provided.

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Section: Introductionsupporting

confidence: 55%

“…In this section we give a few more applications of our study on ideal-representable sequence classes, namely, we generalize results from [22] and [10].…”

Section: Further Applicationsmentioning

confidence: 97%