On the duals of Lp spaces with 0<p<1 |
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Authors: | B Farkas |
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Institution: | 1. Department of Applied Analysis, E?tv?s Loránd University, 1117, Budapest, Pázmány P. Sétány 1/C
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Abstract: | Given a measure space < Ω,m,μ >, a locally bounded, Hausdorff topological linear space < X, τ > and a real number 0<p<1, one can define the space Lp(Ω,m,μ,X), which is, under certain assumptions, a Fréchet space if endowed with a suitable topology. M.M. Day 1] has given a necessary
and sufficient condition, in terms of the properties of the measure space < Ω,m,μ >, for the dual of Lp(Ω,m,μ,C) to be trivial. In this paper a different proof along with a slight generalization is given for this result, using standard
and elementary measure theoretic arguments.
This revised version was published online in June 2006 with corrections to the Cover Date. |
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Keywords: | p-spaces topological dual vector-valued L quasi-normed spaces atoms in measure spaces |
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