Original Articles

L p -valued Measures Without Finite X-semivariation for 2 < p < ∞


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

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