This paper introduces the class of \(\left( p_1,\ldots ,p_m,\sigma ,q,\nu \right) \)-nuclear m-linear operators between Banach spaces, as an intermediate space between the class of nuclear multilinear operators and the whole class of all bounded multilinear operators. The connection with the theory of summing m-linear operators is established. Moreover, we identify this space with a dual space by means of a reasonable crossnorm inspired by the Chevet–Saphar norm.

中文翻译：

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核多线性算子的中级

本文介绍Banach空间之间的\(\left( p_1,\ldots ,p_m,\sigma ,q,\nu \right) \)一核m一线性算子类，作为核多线性类之间的中间空间运算符以及所有有界多线性运算符的整个类。建立了与m-线性算子求和理论的联系。此外，我们通过受 Chevet-Saphar 范数启发的合理交叉范数将该空间识别为对偶空间。