The Truncated Moment Problem for Unital Commutative R-Algebras
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2020
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| _version_ | 1866911766977445888 |
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| author | Curto, Raul E. Ghasemi, Mehdi Infusino, Maria Kuhlmann, Salma |
| author_facet | Curto, Raul E. Ghasemi, Mehdi Infusino, Maria Kuhlmann, Salma |
| contents | 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 classical results on truncated moment problems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2009_05115 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | The Truncated Moment Problem for Unital Commutative R-Algebras Curto, Raul E. Ghasemi, Mehdi Infusino, Maria Kuhlmann, Salma Functional Analysis 44A60, 47A57, 28C05, 46J05, 28E99, 11C99, 60G57 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 classical results on truncated moment problems. |
| title | The Truncated Moment Problem for Unital Commutative R-Algebras |
| topic | Functional Analysis 44A60, 47A57, 28C05, 46J05, 28E99, 11C99, 60G57 |
| url | https://arxiv.org/abs/2009.05115 |