6533b7dbfe1ef96bd126feaa
RESEARCH PRODUCT
Remarks on the semivariation of vector measures with respect to Banach spaces.
Oscar Blascosubject
CombinatoricsDiscrete mathematicsGeneral MathematicsNorm (mathematics)Locally convex topological vector spaceComputingMethodologies_DOCUMENTANDTEXTPROCESSINGBanach spaceInterpolation spaceUniformly convex spaceBanach manifoldLp spaceNormed vector spaceMathematicsdescription
Suppose that and . It is shown that any Lp(µ)-valued measure has finite L2(v)-semivariation with respect to the tensor norm for 1 ≤ p < ∞ and finite Lq(v)-semivariation with respect to the tensor norm whenever either q = 2 and 1 ≤ p ≤ 2 or q > max{p, 2}. However there exist measures with infinite Lq-semivariation with respect to the tensor norm for any 1 ≤ q < 2. It is also shown that the measure m (A) = χA has infinite Lq-semivariation with respect to the tensor norm if q < p.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2007-06-01 | Bulletin of the Australian Mathematical Society |