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Type and cotype of multilinear operators. (English) Zbl 1385.47026
In this paper, the authors introduce the notions of type \((p_1,\dots,p_n)\) and cotype \(q\) for continuous \(n\)-linear operators, extending the classical notion. A finite rank \(n\)-linear operator has any proper cotype only when \(n = 1\)  or \(2\). It is also shown that this type of operators form a Banach ideal.

MSC:
47L22 Ideals of polynomials and of multilinear mappings in operator theory
46G25 (Spaces of) multilinear mappings, polynomials
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