Journal of Operator Theory

Volume 68, Issue 2, Fall 2012 pp. 463-485.

$L^p$-spaces and ideal properties of integration operators for Fréchet-space-valued measures

Authors: R. del Campo (1), S. Okada (2), W.J. Ricker (3)
Author institution: (1) Matematica Aplicada I, Universidad de Sevilla, EUITA, Ctra. de Utrera Km. 1, 41013-Sevilla, Spain
(2) 112 Marconi Crescent, Kambach ACT 2902, Australia
(3) Mathematisch-Geographische Fakultaet, Katholische Universitaet Eichstaett-Ingolstadt, D-85072 Eichstaett, Germany

Summary: An investigation is made of $L^p$-spaces generated by Fréchet-space-valued measures, together with various ideal properties (compactness, weak compactness, complete continuity) of their associated integration map. Such ideal properties influence the nature of the $L^p$-spaces. Significant differences and new features occur which are not present in the Banach space setting.

Keywords: Fréchet space (lattice), vector measure, Fatou property, Lebesgue topology, integration map.

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