Mathematics – Functional Analysis
Scientific paper
2011-11-28
Mathematics
Functional Analysis
Submitted to J. Operator Theory. Typos and wrong expressions corrected, reference added
Scientific paper
We prove a result of extension for linear functionals from a subspace to the whole space with the preservation of a certain strict positivity property. As a consequence we obtain a Riesz-Haviland type result characterizing the existence of the absolutely continuous representing measures in the multivariate truncated moment problems. This property turns to describe the dense interior of the convex cone of all truncated data having representing measures.
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