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Multiple summing operators on Banach spaces. (English) Zbl 1044.46037
There are various methods to generalize properties of linear operators, like compactness, summability, etc., to multilinear operators. In this paper, the authors construct a predual of certain spaces of multiple \((q; p_1,\ldots,p_n)\)-summing multilinear operators. The deduced results are also used to improve several results due to K. Floret and M. C. Matos [Math. Nachr. 176, 65–72 (1995; Zbl 0839.46040)] and Y. Meléndez and A. Tonge [Math. Proc. R. Ir. Acad. 99A, 195–212 (1999; Zbl 0973.46037)] or to give a much easier approach to a result essentially contained in the work of H. P. Rosenthal and S. J. Szarek [Functional analysis, Proc. Semin., Austin/TX (USA) 1987-89, Lect. Notes Math. 1470, 108–132 (1991; Zbl 0758.47022)].

46G25 (Spaces of) multilinear mappings, polynomials
47H60 Multilinear and polynomial operators
47B10 Linear operators belonging to operator ideals (nuclear, \(p\)-summing, in the Schatten-von Neumann classes, etc.)
Full Text: DOI
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