Absolutely summing multilinear operators: a panorama

Pellegrino, Daniel; Santos, Joedson

doi:10.2989/16073606.2011.640459

Cited by 33 publications

(33 citation statements)

References 64 publications

(116 reference statements)

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“…, p n ; p)-dominated multilinear operators, multiple p-summing operators and factorable p-summing operators, among others. [4][5][6][7][8][9][10][11][12][13][14][15] The tensor product point of view is a powerful approach for the study of operator ideals. In particular, the comparison of different topologies on tensor products allows to prove results on their structure and provides characterizations of the most common ideals.…”

Section: Introduction and Basic Definitionsmentioning

confidence: 99%

Traced tensor norms and multiple summing multilinear operators

Rueda

Pérez

Tallab

2016

Linear and Multilinear Algebra

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Using a general tensor norm approach, our aim is to show that some distinguished classes of summing operators can be characterized by means of an 'order reduction' procedure for multiple summing multilinear operators, which becomes the keystone of our arguments and can be considered our main result. We work in a tensor product framework involving traced tensor norms and the representation theorem for maximal operator ideals. Several applications are given not only to multi-ideals, but also to linear operator ideals. In particular, we get applications to multiple p-summing bilinear operators, (p, q)-factorable linear operators, τ (p)-summing linear operators and absolutely p-summing linear operators, providing a characterization of this later class whenever the absolutely p-summing linear operators take values in an L p -space. ARTICLE HISTORY KEYWORDSMultilinear operator; summing operator; multiple summing operator; τ (p)-summing operator; tensor norm

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Section: Introduction and Basic Definitionsmentioning

confidence: 99%

Traced tensor norms and multiple summing multilinear operators

Rueda

Pérez

Tallab

2016

Linear and Multilinear Algebra

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“…In the context of the theory of operator ideals ( [21,22]), it is a natural question whether the class of Cohen (linear) operators forms a complete ideal and also how to generalize this class to multi-ideals and polynomial ideals without loosing the essence of the original ideal. For absolutely summing linear operators there are several types of extensions (e. g. [10,15]). We mention [3], [5], [6], [7], [18] as attempts to establish general criteria that the ideals should possess to preserve properties of the linear ideal.…”

Section: Introductionmentioning

confidence: 99%

Cohen and multiple Cohen strongly summing multilinear operators

Campos

2013

Linear and Multilinear Algebra

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“…The theory of almost summing operators has a strong connection with the well-known theory of absolutely summing operators. For details on almost summing operators we refer to the excellent monograph [17], for recent results we mention [4,24,33] and for classical results on absolutely summing linear operators we refer to [15,17] and references therein; for recent results on linear (and nonlinear) absolutely summing operators we refer to [1,2,7,13,14,19,20,26,27] and to [16] for a modern approach to Grothendieck's Resume´and the roots of the theory of absolutely summing operators.…”

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confidence: 99%