Closed injective ideals of multilinear operators, related measures and interpolation

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...

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Bibliographic Details
Published in:Mathematische Nachrichten 2020-03, Vol.293 (3), p.510-532
Main Authors: Manzano, Antonio, Rueda, Pilar, Sánchez‐Pérez, Enrique A.
Format: Article
Language:English
Subjects:
46G25
closed ideal
ideal of multilinear operators
injective ideal
Interpolation
Linear operators
measure associated to an ideal
Primary: 47L22
Secondary: 46B70
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Summary: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.
ISSN:0025-584X
1522-2616
DOI:10.1002/mana.201800415