Traced tensor norms and multiple summing multilinear operators

Two new classes of summing multilinear operators, factorable (q, p)-summing operators and (r; p, q)-summing operators are studied. These classes are described in terms of factorization. It is shown that operators in the first (resp., the second) class admit the factorization through the injective tensor product of Banach spaces (resp., through some Banach lattices). Applications in different contexts related to Grothendieck Theorem and Fourier integral bilinear operators are shown. Motivated by Pisier's Theorem on factorization of (q, 1)-summing operators from C(K)-spaces through Lorentz spaces Lq,1 on some probability Borel measure spaces, we prove two variants of Pisier's Theorem for bilinear operators on the product of C(K)-spaces. We also prove bilinear versions of Mityagin-Pe lczyński and Kislyakov Theorems.

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“…associated to the linear operator S : X → Y . Recently, more properties and applications of these operators have been studied in [34].…”

Section: Factorable (Q P)-summing Multilinear Operatorsmentioning

confidence: 99%

Factorization theorems for some new classes of multilinear operators

Mastyło

Pérez

2020

Asian Journal of Mathematics

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“…In [25] tensor products have been used to characterize summability properties of linear and multilinear operators by means of an "order reduction" procedure and the calculus of traced tensor norms. The map P is the restriction to the diagonal of the m-linear symmetric operator…”

Section: Associated Polynomialsmentioning

confidence: 99%

Tensor Characterizations of Summing Polynomials

et al. 2018

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Operators T that belong to some summing operator ideal, can be characterized by means of the continuity of an associated tensor operator T that is defined between tensor products of sequences spaces. In this paper we provide a unifying treatment of these tensor product characterizations of summing operators. We work in the more general frame provided by homogeneous polynomials, where an associated "tensor" polynomial-which plays the role of T-, needs to be determined first. Examples of applications are shown.

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“…for all continuous bilinear forms . For recent results on absolutely summing linear and multilinear operators see [3,4,5].…”

Section: Introductionmentioning

confidence: 99%

The Orlicz Inequality for Series of Multilinear Forms

Salih

Hussein

2022

JAMCS

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The Orlicz ( \(\ell\)2,\(\ell\)1)-mixed inequality of integers and fractional dimensions who states that, with a bit of extend, for all sequences of bilinear forms AL: \(\mathbb{K}\)n x \(\mathbb{K}\)n \(\rightarrow\) \(\mathbb{K}\) and all positive integers n, where \(\mathbb{K}\)n denotes \(\mathbb{R}\)n or \(\mathbb{C}\)n endowed with the supremum norm. For that we follow D.Núñez-Alarcón, D. Pellegrino, and D. Serrano-Rodríguez [1]] to extend this inequality to series of multilinear forms, with \(\mathbb{K}\)n endowed with \(\ell\)1+ \(\epsilon\) norms for all successive gradually of the general 0 ≤ ϵ ≤ ∞.

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Traced tensor norms and multiple summing multilinear operators

Cited by 7 publications

References 21 publications

Factorization theorems for some new classes of multilinear operators

Factorization theorems for some new classes of multilinear operators

Tensor Characterizations of Summing Polynomials

The Orlicz Inequality for Series of Multilinear Forms

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