In this paper we introduce a function for multilinear operators that can be considered as an extension of the so-called outer measure associated to a linear operator ideal. We prove that it allows to characterize the operators that belong to a closed surjective ideal of multilinear operators as those having measure equal to zero. We also obtain some interpolation formulas for this new measure. As a consequence we deduce interpolation results for arbitrary closed surjective ideals of multilinear operators which recover, in particular, different results previously established in the literature.

中文翻译：

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多线性算子和插值的封闭形容理想

在本文中，我们介绍了一种用于多线性算子的函数，该函数可以看作是与线性算子理想相关的外部度量的扩展。我们证明，它可以将属于多线性算子的封闭式排斥理想的算子表征为度量为零的算子。我们还为该新度量获取了一些插值公式。结果，我们推导出了针对多线性算子的任意封闭外射理想的插值结果，这些插值理想地恢复了先前文献中建立的不同结果。