Nonlinear absolutely summing operators revisited

In the last decades many authors have become interested in the study of multilinear and polynomial generalizations of families of operator ideals (such as, for instance, the ideal of absolutely summing operators). However, these generalizations must keep the essence of the given operator ideal and t...

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Bibliographic Details
Published in:Boletim da Sociedade Brasileira de Matemática 2015-06, Vol.46 (2), p.205-249
Main Authors: Bernardino, A. T., Pellegrino, D., Seoane-Sepúlveda, J. B., Souza, M. L. V.
Format: Article
Language:English
Subjects:
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Theoretical
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Summary:In the last decades many authors have become interested in the study of multilinear and polynomial generalizations of families of operator ideals (such as, for instance, the ideal of absolutely summing operators). However, these generalizations must keep the essence of the given operator ideal and there seems not to be a universal method to achieve this. The main task of this paper is to discuss, study, and introduce multilinear and polynomial extensions of the aforementioned operator ideals taking into account the already existing methods of evaluating the adequacy of such generalizations. Besides this subject’s intrinsic mathematical interest, the main motivation is our belief (based on facts that shall be presented) that some of the already existing approaches are not adequate.
ISSN:1678-7544
1678-7714
DOI:10.1007/s00574-015-0091-0