Virtually (r; r_1, ... , r_n ; s)-nuclear multilinear operators

Autores/as

  • Dahmane Achour, University of M'sila, 28000 M'sila, Algeria,
  • Amar Belacel University of Laghouat, 03000 Laghouat, Algeria

DOI:

https://doi.org/10.17398/

Palabras clave:

Multilinear operators, nuclear operators, summing operators

Resumen

In this paper, the space of virtually (r; r_1, ... , r_n; s)-nuclear multilinear operators between Banach spaces is introduced, some of its properties are described and its topological dual is characterized as a Banach space of multiple absolutely (r'; r'_1, ... , r'_n; s')-summing multilinear operators.

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Referencias

D. Achour, Multilinear extensions of absolutely (p; q; r)-summing operators. Rend. Circ. Mat. Palermo (2) 60 (3) (2011), 337-350.

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B.M. Cerna, “Operadores Multilinears p-fatoraveis”, PhD, UMICAMP, Campinas, 2005.

B.M. Cerna, Some properties of multi-linear operators F nuclear type, Int. J. Pur. Appl. Math. 56 (1) (2009), 143-154.

C.P. Gupta, On the Malgrange theorem for nuclearly entire functions of bounded type on a Banach space, Indag. Math. (Proceedings) 73 (1970), 356-358.

J.T. Lapresté, Op´erateurs sommants et factorisations `a travers les espaces Lp, Studia Math. 57 (1) (1976), 47-83.

B. Malgrange, Existence et approximation des solutions des equations aux d´eriv´ees partielles et des ´equations des convolutions, Ann. Inst. Fourier, Grenoble, 6 (1955/56), 271-355.

M.C. Matos, On multilinear mappings of nuclear type, Rev. Mat Univ. Complut. Madrid. 6 (1) (1993), 61-81.

M.C. Matos, Fully absolutely summing and Hilbert-Schmidt multilinear mappings, Collect. Math. 54 (2) (2003), 111-136.

M.C. Matos, “Absolutely Summing Mappings, Nuclear Mappings and Convolution Equations”, Relat orio, IMECC-UNICAMP, 2007.

A. Pietsch, “Operator Ideals”, Deutscher Verlag der Wissenschaften, Berlin, 1978; North-Holland, Amsterdam-London-New York-Tokyo, 1980.

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Publicado

2015-12-01

Número

Sección

Operator Theory

Cómo citar

Virtually (r; r_1, ... , r_n ; s)-nuclear multilinear operators. (2015). Extracta Mathematicae, 30(2), 235-250. https://doi.org/10.17398/