On the determinacy of the moment problem for symmetric algebras of a locally convex space

Abstract

This note aims to show a uniqueness property for the solution (whenever exists) to the moment problem for the symmetric algebra $S(V)$ of a locally convex space $(V,\tau )$. Let $\mu$ be a measure representing a linear functional $L:S(V)\to \mathbb{R}$. We deduce a sufficient determinacy condition on $L$ provided that the support of $\mu$ is contained in the union of the topological duals of $V$ w.r.t. to countably many of the seminorms in the family inducing $\tau$. We compare this result with some already known in literature for such a general form of the moment problem and further discuss how some prior knowledge on the support of the representing measure influences its determinacy.

7 pages, note in memory of M. Marshall, minor corrections, acknowledgements added, update references

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• The full infinite dimensional moment problem on semi-algebraic sets of generalized functions
• The Moment Problem for Continuous Positive Semidefinite Linear functionals
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Cited by in corpus (1)

• On the classification of function algebras on subvarieties of noncommutative operator balls