Nonlinear absolutely summing operators revisited

Autor:	Marcela L.V. Souza, Adriano Thiago Bernardino, Daniel Pellegrino, Juan B. Seoane-Sepúlveda
Rok vydání:	2015
Předmět:	Nonlinear system Multilinear map Pure mathematics Polynomial Operator ideal Ideal (set theory) Operator (computer programming) General Mathematics Subject (grammar) Calculus Task (project management) Mathematics
Zdroj:	Bulletin of the Brazilian Mathematical Society, New Series. 46:205-249
ISSN:	1678-7714 1678-7544
DOI:	10.1007/s00574-015-0091-0
Popis:	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.
Databáze:	OpenAIRE
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