Quasi s-numbers and measures of non-compactness of multilinear operators

Fernandez, Dicesar Lass; Mastyło, Mieczysław; Silva, Eduardo B. da

doi:10.5186/aasfm.2013.3842

Cited by 5 publications

(6 citation statements)

References 13 publications

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“…By Lemma 8.5, there is R : Y → 2 such that R * = V . Thus, by [5,Proposition 3.2], we obtain a n (T × V ) = a n (T × R * ) = a n ((RT ) × ) ≤ a (k) n (RT ) ≤ sup{a (k) n (ST ); S : Y → 2 ≤ 1} = y (k) n (T ). (ii).…”

Section: Lemma 85mentioning

confidence: 99%

“…Now, we are ready to introduce a modified variant of the notion of s-numbers in the setting of k-linear operators, which appeared in [5].…”

Section: S-numbers Of Multilinear Operatorsmentioning

confidence: 99%

“…While the properties of s-numbers of linear operators are well-known, Pietsch's research problem on a theory of s-numbers of multilinear operators had not been studied extensively. This is the main motivation to continue the study of variants of s-numbers in the context of multilinear operators initiated in the paper [5] and continued in [1] in the setting of polynomials acting between Banach spaces.…”

Section: Introductionmentioning

confidence: 99%

“…2, we introduce a modified variant of the notion of s-numbers in the setting of k-linear operators. This notion is more general that the one given in [5]. We also introduce the notion of symmetric, injective, surjective s (k) scale, and also the mixed multiplicative property.…”

Section: Introductionmentioning

confidence: 99%

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Pietsch’s variants of s-numbers for multilinear operators

Fernandez

Mastyło

Silva

2021

Rev. Real Acad. Cienc. Exactas Fis. Nat. Ser. A-Mat.

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We study variants of s-numbers in the context of multilinear operators. The notion of an $$s^{(k)}$$ s ( k ) -scale of k-linear operators is defined. In particular, we shall deal with multilinear variants of the $$s^{(k)}$$ s ( k ) -scales of the approximation, Gelfand, Hilbert, Kolmogorov and Weyl numbers. We investigate whether the fundamental properties of important s-numbers of linear operators are inherited to the multilinear case. We prove relationships among some $$s^{(k)}$$ s ( k ) -numbers of k-linear operators with their corresponding classical Pietsch’s s-numbers of a generalized Banach dual operator, from the Banach dual of the range space to the space of k-linear forms, on the product of the domain spaces of a given k-linear operator.

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Section: Lemma 85mentioning

confidence: 99%

“…Now, we are ready to introduce a modified variant of the notion of s-numbers in the setting of k-linear operators, which appeared in [5].…”

Section: S-numbers Of Multilinear Operatorsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Pietsch’s variants of s-numbers for multilinear operators

Fernandez

Mastyło

Silva

2021

Rev. Real Acad. Cienc. Exactas Fis. Nat. Ser. A-Mat.

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“…Terzioğlu's characterization for compact maps found its use in more current research on compact maps as well. See [9,10,18].…”

Section: Corollary 25 ( [20])mentioning

confidence: 99%

On a theorem of Terzioğlu

Aksoy¹

2019

Turk J Math

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The theory of compact linear operators acting on a Banach space has a classical core and is familiar to many. Perhaps less known is the characterization theorem of Terzioğlu for compact maps. This theorem has a number of important connections that deserves illumination. In this paper we survey Terzioğlu's characterization theorem for compact maps and some of its consequences. We also prove a similar characterization theorem for Q -compact maps.

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Closed surjective ideals of multilinear operators and interpolation

Manzano

Rueda

Pérez

2021

Banach J. Math. Anal.

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We introduce and discuss several ways of extending the inner measure arisen from the closed injective hull of an ideal of linear operators to the multilinear case. In particular, we consider new measures that allow to characterize the operators that belong to a closed injective ideal of multilinear operators as those having measure equal to zero. Some interpolation formulas for these measures, and consequently interpolation results involving ideals of multilinear operators, are established. Examples and applications related to summing multilinear operators are also shown. Ideal of multilinear operators, closed ideal, injective ideal, measure associated to an ideal, interpolation MSC Primary: 47L22; Secondary: 46B70, 46G25.

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Quasi s-numbers and measures of non-compactness of multilinear operators

Cited by 5 publications

References 13 publications

Pietsch’s variants of s-numbers for multilinear operators

Pietsch’s variants of s-numbers for multilinear operators

On a theorem of Terzioğlu

Closed surjective ideals of multilinear operators and interpolation

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