Strongly p-summing multilinear operators

Dimant, Verónica

doi:10.1016/s0022-247x(02)00710-2

Cited by 72 publications

(81 citation statements)

References 2 publications

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“…The strongly p-summing multilinear operators of Dimant (see [8]) are also related with our class, but in this case only n 2 = 1 is allowed in the inequalities considered in the definition.…”

Section: Let Us Consider Now the Quotient Mapmentioning

confidence: 99%

“…However, the main achievements to find abstract domination theorems inspired in absolutely summing operators are not accompanied by general factorization theorems. It is known that although for some classes of multilinear mappings a domination theorem holds, it is sometimes not clear whether this can be written as a standard factorization (see [8,15]). Some progress was made in [15,21], where the tandem domination/factorization for classes of summing polynomials and multilinear operators was orchestrated.…”

Section: Introductionmentioning

confidence: 99%

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Domination spaces and factorization of linear and multilinear summing operators

Achour

Dahia

Rueda

et al. 2016

Quaestiones Mathematicae

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Abstract. It is well known that not every summability property for multilinear operators leads to a factorization theorem. In this paper we undertake a detailed study of factorization schemes for summing linear and nonlinear operators. Our aim is to integrate under the same theory a wide family of classes of mappings for which a Pietsch type factorization theorem holds. Our construction includes the cases of absolutely p-summing linear operators, (p, σ)-absolutely continuous linear operators, factorable strongly p-summing multilinear operators, (p1, . . . , pn)-dominated multilinear operators and dominated (p1, . . . , pn; σ)-continuous multilinear operators.

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Section: Let Us Consider Now the Quotient Mapmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Domination spaces and factorization of linear and multilinear summing operators

Achour

Dahia

Rueda

et al. 2016

Quaestiones Mathematicae

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“…This terminology was introduced in the commutative case by Pietsch [19] for scalar valued mappings. The reader interested by previous work on this and related properties can consult [3,5,6,7,8,13,14,16,17].…”

Section: Basic Definitions and Propertiesmentioning

confidence: 99%

Characterization of lr-dominated m-linear operators

Mezrag¹

2010

Demonstratio Mathematica

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Abstract. In this paper, we define and study a new concept of r-dominated multilinear operators in the category of operator spaces, which we call l r -dominated m-linear operators. We give some characterizations of this concept such as the theorem of factorization. IntroductionThe concept of r-dominated multilinear operators was mainly introduced at the beginning of the 1980s by Pietsch [19] where the idea of generalizing the theory of ideals of linear operators to the multilinear setting appears. Motivated by the importance of this theory, several authors have developed and studied many concepts relating to summability (we mention for example [13,14,16,18] among so many authors). Regarding this, it is natural to try to develop analogous in the noncommutative case. Hence, this paper deals with the equivalent of this concept in the theory of operator spaces; which will be called the "l r -dominated m-linear operators". Firstly, we will introduce the notion of l r -dominated m-linear operators and we prove an analogue to the Pietsch domination theorem. After that, we shall give the factorization theorem of such operators. We finish this paper by giving the finite dimensional version of our result. This paper is organized as follows.In the first section, we recall some basic definitions and properties concerning the theory of operator spaces.In the second section of the present paper, we introduce and study the notion of l r -dominated multilinear operators. We give the Pietsch domination theorem and related properties.2000 Mathematics Subject Classification: 46B28, 47H60, 46G25, 46B25. Key words and phrases: completely bounded operator, l r -dominated multilinear operator, operator space, Pietsch domination theorem. Brought to you by | MIT LibrariesAuthenticated

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“…Strongly summing multilinear mappings were introduced by V. Dimant [17] for real Banach spaces, but complex scalars work for our purposes as well. The spaces of all semi-integral, dominated and strongly summing n-linear mappings from…”

Section: Proof (A) Sincementioning

confidence: 99%

“…, E n ; F ), respectively. These spaces become Banach spaces with the semi-integral, dominated and strongly summing norms, which definitions can be found in [2], [24] and [17], respectively.…”

Section: Proof (A) Sincementioning

confidence: 99%

On Composition Ideals of Multilinear Mappings and Homogeneous Polynomials

Botelho¹,

Pellegrino²,

Rueda³

2007

Publ. Res. Inst. Math. Sci.

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Given an operator ideal I, we study the multi-ideal I • L and the polynomial ideal I • P. The connection with the linearizations of these mappings on projective symmetric tensor products is investigated in detail. Applications to the ideals of strictly singular and absolutely summing linear operators are obtained. §1. Introduction Since the 1983 paper by A. Pietsch [26], ideals of multilinear mappings (multi-ideals) and homogeneous polynomials (polynomial ideals) between Banach spaces have been studied as a natural consequence of the successful theory of operator ideals. Several ideals have been investigated and abstract methods to generate ideals of multilinear mappings and polynomials have been introduced (see [6,20]

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Strongly p-summing multilinear operators

Cited by 72 publications

References 2 publications

Domination spaces and factorization of linear and multilinear summing operators

Domination spaces and factorization of linear and multilinear summing operators

Characterization of lr-dominated m-linear operators

On Composition Ideals of Multilinear Mappings and Homogeneous Polynomials

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