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Absolutely summing multilinear operators: a panorama. (English) Zbl 1274.47001
This paper has a twofold purpose: to present an overview of the theory of absolutely summing operators and its different generalizations for the multilinear setting, and to sketch the beginning of a research project related to an objective search of “perfect” multilinear extensions of the ideal of absolutely summing operators. The final section contains some open problems that may indicate lines for future investigation.

MSC:
47-02 Research exposition (monographs, survey articles) pertaining to operator theory
47B10 Linear operators belonging to operator ideals (nuclear, \(p\)-summing, in the Schatten-von Neumann classes, etc.)
47L22 Ideals of polynomials and of multilinear mappings in operator theory
46G25 (Spaces of) multilinear mappings, polynomials
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