Multiple summing operators on Banach spaces.
type: Item
instance of: scholarly article
title: Multiple summing operators on Banach spaces.
zbMATH Open document ID: 1044.46037
DOI: 10.1016/S0022-247X(03)00352-4
author: David Pérez-García
author: Ignacio Villanueva
published in: Journal of Mathematical Analysis and Applications
publication date: 2003-09-25T00:00:00Z
review text: 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 \textit{K. Floret} and \textit{M. C. Matos} [Math. Nachr. 176, 65--72 (1995; Zbl 0839.46040)] and \textit{Y. Meléndez} and \textit{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 \textit{H. P. Rosenthal} and \textit{S. J. Szarek} [Functional analysis, Proc. Semin., Austin/TX (USA) 1987-89, Lect. Notes Math. 1470, 108--132 (1991; Zbl 0758.47022)].
Mathematics Subject Classification ID: 46G25
Mathematics Subject Classification ID: 47H60
Mathematics Subject Classification ID: 47B10
zbMATH DE Number: 1985890
zbMATH Keywords: \(p\)-summing multilinear operators
zbMATH Keywords: \(r\)-dominated multilinear operators
zbMATH Keywords: integral multilinear operators
Wikidata QID: Q59474407
reviewed by: Hans-Andreas Braunß
MaRDI profile type: Publication
cites work: Multilinear Mappings of Nuclear and Integral Type
cites work: Estimates by polynomials
cites work: Polynomial characterization of \({\mathcal L}_{\infty}\)-spaces
cites work: Schatten-von Neumann classes of multilinear forms
cites work: Q4023934
cites work: Q4850055
cites work: Partial differential equations in Fischer-Fock spaces for the Hilbert-Schmidt holomorphy type
cites work: Ultrastability of ideals of homogeneous polynomials and multilinear mappings on Banach spaces
cites work: Application of a Khintchine Inequality to Holomorphic Mappings
cites work: Fully, absolutely summing and Hilbert-Schmidt multilinear mappings
cites work: Q4296472
cites work: Q4521235
cites work: Multiple summing operators on \(C(K)\) spaces
cites work: Q3675026
cites work: Operator ideals and spaces of bilinear operators
cites work: Q3975984
cites work: Integral mappings between Banach spaces
description: scientific article; zbMATH DE number 1985890