An operator-valued moment problem
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- Proc. Amer. Math. Soc. 112 (1991), 1023-1028 Request permission
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
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- Mihai Putinar, The $L$ problem of moments in two dimensions, J. Funct. Anal. 94 (1990), no. 2, 288–307. MR 1081646, DOI 10.1016/0022-1236(90)90015-D
- Donald Sarason, Moment problems and operators in Hilbert space, Moments in mathematics (San Antonio, Tex., 1987) Proc. Sympos. Appl. Math., vol. 37, Amer. Math. Soc., Providence, RI, 1987, pp. 54–70. MR 921084, DOI 10.1090/psapm/037/921084 F. H. Vasilescu, Introducere in teoria operatorilor liniari, Editura Tehnicā, 1987.
Additional Information
- © Copyright 1991 American Mathematical Society
- 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