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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.


References [Enhancements On Off] (What's this?)

  • [1] N. I. Achiezer and M. G. Krein, Some questions in the theory of moments, Amer. Math. Soc., Providence, RI, 1962. MR 0167806 (29:5073)
  • [2] R. W. Carey, Unitary invariant for self-adjoint operators, 1973.
  • [3] M. Putinar, A $ L$-problem of moments in two-dimensions, preprint, 1988. MR 1081646 (91m:47018)
  • [4] D. Sarason, Moment problems and operators in Hilbert space, Proc. Sympos. Appl. Math., vol. 37, Amer. Math. Soc., Providence, RI, 1987, p. 54. MR 921084 (89g:47008)
  • [5] F. H. Vasilescu, Introducere in teoria operatorilor liniari, Editura Tehnicā, 1987.

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Additional Information

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

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