Search results for "Multilinear operator"

showing 3 items of 3 documents

Closed injective ideals of multilinear operators, related measures and interpolation

2020

[EN] 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.

Multilinear mapPure mathematicsIdeal (set theory)Ideal of multilinear operatorsGeneral MathematicsZero (complex analysis)Measure associated to an idealMeasure (mathematics)Injective functionInterpolationClosed idealInjective idealInner measureInjective hullMATEMATICA APLICADAInterpolationMathematics
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Traced tensor norms and multiple summing multilinear operators

2016

[EN] 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, tau(p)-summing linear operators and absolutely p-summing li…

Multilinear mapAlgebra and Number Theory010102 general mathematicsTensor norm010103 numerical & computational mathematicsSpectral theoremSumming operatorOperator theoryMultiple summing operator01 natural sciencesFourier integral operatorQuasinormal operatorAlgebraLinear mapMultilinear operatorTensor product0101 mathematicsMATEMATICA APLICADAOperator normtau(p)-Summing operatorMathematics
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Factorization of strongly (p,sigma)-continuous multilinear operators

2013

We introduce the new ideal of strongly-continuous linear operators in order to study the adjoints of the -absolutely continuous linear operators. Starting from this ideal we build a new multi-ideal by using the composition method. We prove the corresponding Pietsch domination theorem and we present a representation of this multi-ideal by a tensor norm. A factorization theorem characterizing the corresponding multi-ideal - which is also new for the linear case - is given. When applied to the case of the Cohen strongly -summing operators, this result gives also a new factorization theorem.

Unbounded operatorDiscrete mathematicsMultilinear mapPrimary 46A32Algebra and Number TheoryMathematics::Commutative AlgebraTensor normSpectral theoremOperator theoryPietsch domination theoremMultilinear operatorsymbols.namesakeFactorizationNorm (mathematics)Weierstrass factorization theoremsymbolsSecondary 47B10FactorizationMATEMATICA APLICADAOperator normAbsolutely continuous operatorsMathematics
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