We investigate when a linear functional L defined on a linear subspace B of a unital commutative real algebra A admits an integral representation w.r.t. a positive Radon measure supported on a closed subset K of the character space of A. We provide a criterion for the existence of such a representation for L when A is equipped with a submultiplicative seminorm. We then build on this result to prove our main theorem for A not necessarily equipped with a topology. This allows us to extend well-known results on truncated moment problems.

The Truncated Moment Problem for Unital Commutative R-Algebras

Maria Infusino;
2023-01-01

Abstract

We investigate when a linear functional L defined on a linear subspace B of a unital commutative real algebra A admits an integral representation w.r.t. a positive Radon measure supported on a closed subset K of the character space of A. We provide a criterion for the existence of such a representation for L when A is equipped with a submultiplicative seminorm. We then build on this result to prove our main theorem for A not necessarily equipped with a topology. This allows us to extend well-known results on truncated moment problems.
2023
Truncated moment problem; Full moment problem; Measure; Integral representation; Linear functional
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11584/352404
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