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Lp-valued measures without finite X-semivariation for 2 < p < ∞


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Opened Access Lp-valued measures without finite X-semivariation for 2 < p < ∞
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Author: Jefferies, Brian
Okada, Susumu
Rodríguez Piazza, Luis
Department: Universidad de Sevilla. Departamento de Análisis Matemático
Date: 2007
Published in: Quaestiones Mathematicae, 30 (4), 437-449.
Document type: Article
Abstract: We show that for 1 ≤ p < ∞, the property that every Lp-valued vector measure has finite X-semivariation in Lp(μ, X) is equivalent to the property that every continuous linear map from 1 to X is p-summing. For 2 < p < ∞, we explicitly construct an Lp([0, 1])-valued measure without finite Lp-semivariation.
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