Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 38, 2013, 805-823
Universidade Estadual de Campinas - Unicamp, Instituto de Matemática
Campinas, São Paulo, 13083-859, Brazil; dicesar 'at' ime.unicamp.br
Adam~Mickiewicz University, Faculty of Mathematics & Computer Science
and Polish Academy of Science (Poznan branch), Institute of Mathematics
Umultowska 87, 61-614 Poznan, Poland; mastylo 'at' amu.edu.pl
Universidade Estadual de Maringá - UEM, Departamento de Matemática
Av. Colombo 5790, Maringá, Paraná, 870300-110, Brazil; ebsilva 'at' wnet.com.br
Abstract. The main goal of this paper is the study of quasi s-numbers of multilinear operators among Banach spaces. The relationships among multilinear variants of approximation, Kolmogorov and Gelfand numbers of operators and their generalized linear adjoint are shown. In the multilinear case, analogous theorems which are well-known in the linear case, are stated and proved. The estimates of measures of non-compactness of multilinear operators in terms of measures of the adjoint operators are also proved.
2010 Mathematics Subject Classification: Primary 46G25, 47A07, 47B06.
Key words: Multilinear operator, s-numbers, approximation, Gelfand, Kolmogorov numbers, the measure of non-compactness.
Reference to this article: D.L. Fernandez, M. Mastylo and E.B. da Silva: Quasi s-numbers and measures of non-compactness of multilinear operators. Ann. Acad. Sci. Fenn. Math. 38 (2013), 805-823.
doi:10.5186/aasfm.2013.3842
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