Geodesic
Approximation of integration maps of vector measures and limit representations of Banach function spaces
Eduardo Jiménez Fernández1 ; Enrique A. Sánchez Pérez2 ; Dirk Werner3
1 Departamento de Economía Universitat Jaume I Campus del Riu Sec, s/n 12071 Castelló de la Plana, Spain
2 Instituto Universitario de Matemática Pura y Aplicada Universitat Politècnica de València Camino de Vera, s/n 46022 València, Spain
3 Fachbereich Mathematik und Informatik Freie Universität Berlin Arnimallee 6 14195 Berlin, Germany
Annales Polonici Mathematici, Tome 120 (2017) no. 1, pp. 63-81 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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We study whether or not the integration maps of vector measures can be computed as pointwise limits of their finite rank Radon–Nikodým derivatives. The positive cases are obtained by using the circle of ideas related to the approximation property for Banach spaces. The negative ones are given by means of an appropriate use of the Daugavet property. As an application, we analyse when the norm in a space $L^1(m)$ of integrable functions can be computed as a limit of the norms of the spaces of integrable functions with respect to the Radon–Nikodým derivatives of $m$.
DOI : 10.4064/ap170407-21-9
Keywords: study whether integration maps vector measures computed pointwise limits their finite rank radon nikod derivatives positive cases obtained using circle ideas related approximation property banach spaces negative given means appropriate daugavet property application analyse norm space integrable functions computed limit norms spaces integrable functions respect radon nikod derivatives nbsp

Eduardo Jiménez Fernández 1 ; Enrique A. Sánchez Pérez 2 ; Dirk Werner 3

1 Departamento de Economía Universitat Jaume I Campus del Riu Sec, s/n 12071 Castelló de la Plana, Spain
2 Instituto Universitario de Matemática Pura y Aplicada Universitat Politècnica de València Camino de Vera, s/n 46022 València, Spain
3 Fachbereich Mathematik und Informatik Freie Universität Berlin Arnimallee 6 14195 Berlin, Germany 
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Eduardo Jiménez Fernández; Enrique A. Sánchez Pérez; Dirk Werner. Approximation of integration maps of vector measures and limit representations of Banach function spaces. Annales Polonici Mathematici, Tome 120 (2017) no. 1, pp. 63-81. doi: 10.4064/ap170407-21-9

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