Search results for "Pietsch domination theorem"

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A unified Pietsch domination theorem

2008

In this paper we prove an abstract version of Pietsch's domination theorem which unify a number of known Pietsch-type domination theorems for classes of mappings that generalize the ideal of absolutely p-summing linear operators. A final result shows that Pietsch-type dominations are totally free from algebraic conditions, such as linearity, multilinearity, etc.

Discrete mathematicsMathematics::Functional AnalysisDomination analysisApplied MathematicsLinear operatorsBanach spacePietsch domination theoremFunctional Analysis (math.FA)Linear mapMathematics - Functional AnalysisBanach spacesFOS: MathematicsIdeal (order theory)Algebraic numberAbsolutely summing mappingsAnalysisMathematicsJournal of Mathematical Analysis and Applications
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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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