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Remarks on the semivariation of vector measures with respect to Banach spaces.

Published online by Cambridge University Press:  17 April 2009

Oscar Blasco
Oscar Blasco
Affiliation:
Department of Mathematics, Universitat de Valencia, Burjassot 46100 (Valencia), Spain, e-mail: oscar.blasco@uv.es
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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.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 75 , Issue 3 , June 2007 , pp. 469 - 480
Copyright
Copyright © Australian Mathematical Society 2007

References

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