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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Published inBoletim da Sociedade Brasileira de Matemática Vol. 46; no. 2; pp. 205 - 249
Main Authors Bernardino, A. T., Pellegrino, D., Seoane-Sepúlveda, J. B., Souza, M. L. V.
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.06.2015
Subjects
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Theoretical
polynomial ideals
absolutely summing operators
coherent ideals
compatible ideals
47B10
47H60
46G25
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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