Lp-Valued measures without finite x-semivariation for 2 < p < ∞

Brian Jefferies; Susumu Okada; Luis Rodríguez-Piazza

doi:10.2989/16073600709486211

L^p-Valued measures without finite x-semivariation for 2 < p < ∞

Brian Jefferies, Susumu Okada, Luis Rodríguez-Piazza

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

We show that for 1 ≤ p < ∞, the property that every L^p-valued vector measure has finite X-semivariation in L^p(μ, X) is equivalent to the property that every continuous linear map from l¹to X is p-summing. For 2 < p < ∞, we explicitly construct an L^p([0, 1])-valued measure without finite L^p-semivariation.

Original language	English
Pages (from-to)	437-449
Number of pages	13
Journal	Quaestiones Mathematicae
Volume	30
Issue number	4
DOIs	https://doi.org/10.2989/16073600709486211
Publication status	Published - 1 Jul 2007

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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 l1to X is p-summing. For 2 < p < ∞, we explicitly construct an Lp([0, 1])-valued measure without finite Lp-semivariation.",

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L^p-Valued measures without finite x-semivariation for 2 < p < ∞

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