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- W4295774141 abstract "Kiukas, Lahti and Ylinen asked the following general question. When is a positive operator measure projection valued? A version of this question formulated in terms of operator moments was posed in a recent paper of the present authors. Let $T$ be a selfadjoint operator and $F$ be a Borel semispectral measure on the real line with compact support. For which positive integers $p< q$ do the equalities $T^k =int_{mathbb{R}} x^k F(dx)$, $k=p, q$, imply that $F$ is a spectral measure? In the present paper, we completely solve the second problem. The answer is affirmative if $p$ is odd and $q$ is even, and negative otherwise. The case $(p,q)=(1,2)$ closely related to intrinsic noise operator was solved by several authors including Kruszy'{n}ski and de Muynck as well as Kiukas, Lahti and Ylinen. The counterpart of the second problem concerning the multiplicativity of unital positive linear maps on $C^*$-algebras is also solved." @default.
- W4295774141 created "2022-09-15" @default.
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- W4295774141 date "2021-03-17" @default.
- W4295774141 modified "2023-09-25" @default.
- W4295774141 title "Two-moment characterization of spectral measures on the real line" @default.
- W4295774141 doi "https://doi.org/10.48550/arxiv.2103.09964" @default.
- W4295774141 hasPublicationYear "2021" @default.
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