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Nonlinear absolutely summing operators revisited

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Bernardino, Adriano Thiago and Pellegrino, Daniel and Seoane-Sepúlveda, Juan B. and Souza, Marcela L.V. (2015) Nonlinear absolutely summing operators revisited. Bulletin of the Brazilian Mathematical Society, New Series, 46 (2). pp. 205-249. ISSN 1678-7544

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Official URL: http://link.springer.com/article/10.1007/s00574-015-0091-0


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Abstract

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.


Item Type:Article
Uncontrolled Keywords:absolutely summing operators; coherent ideals; compatible ideals; polynomial ideals
Subjects:Sciences > Mathematics > Functional analysis and Operator theory
ID Code:36215
Deposited On:01 Apr 2016 11:54
Last Modified:29 Nov 2016 09:09

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