Bounded sets in the range of an X ∗ ∗ -valued measure with bounded variation

B. Marchena and C. Piñeiro

International Journal of Mathematics and Mathematical Sciences, 2000, vol. 23, 1-10

Abstract:

Let X be a Banach space and A ⊂ X an absolutely convex, closed, and bounded set. We give some sufficient and necessary conditions in order that A lies in the range of a measure valued in the bidual space X ∗ ∗ and having bounded variation. Among other results, we prove that X ∗ is a G. T.-space if and only if A lies inside the range of some X ∗ ∗ -valued measure with bounded variation whenever X A is isomorphic to a Hilbert space.

Date: 2000
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:390761

DOI: 10.1155/S0161171200001708

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