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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

An operator-valued moment problem


Author: Luminiţa Lemnete
Journal: Proc. Amer. Math. Soc. 112 (1991), 1023-1028
MSC: Primary 47A57; Secondary 44A60
DOI: https://doi.org/10.1090/S0002-9939-1991-1059628-5
MathSciNet review: 1059628
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Abstract: We link Carey's exponential representation of the determining function of a perturbation pair with the moment problem. We prove that an operator sequence represents the moments of a phase operator if and only if there is another positively defined sequence of operators satisfying a boundedness condition.


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DOI: https://doi.org/10.1090/S0002-9939-1991-1059628-5
Keywords: $ L$-problem of moments, phase operator, determining function
Article copyright: © Copyright 1991 American Mathematical Society