Closed injective ideals of multilinear operators, related measures and interpolation
Antonio Manzano, Pilar Rueda, Enrique A. Sánchez‐Pérez
Abstract
Abstract 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.
Topics & Concepts
Multilinear mapMathematicsInjective functionInterpolation (computer graphics)Measure (data warehouse)Ideal (ethics)Pure mathematicsOperator theoryDiscrete mathematicsAlgebra over a fieldComputer scienceImage (mathematics)DatabaseEpistemologyArtificial intelligencePhilosophyAdvanced Banach Space TheoryApproximation Theory and Sequence SpacesHolomorphic and Operator Theory