Application of the operator phase shift in the $L$-problem of moments
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Abstract:
This note studies more deeply the results obtained in an earlier paper of the author (An operator-valued moment problem, Proc. Amer. Math. Soc. 112 (1991)). It gives a similar condition for the solvability of the L-problem of moments, using the operator phase shift. Based on this, it underlines some of the aspects of the operator phase shift used in the L-problem of moments.References
- N. I. Aheizer and M. Krein, Some questions in the theory of moments, Translations of Mathematical Monographs, Vol. 2, American Mathematical Society, Providence, R.I., 1962. Translated by W. Fleming and D. Prill. MR 0167806, DOI 10.1090/mmono/002
- Richard W. Carey, A unitary invariant for pairs of self-adjoint operators, J. Reine Angew. Math. 283(284) (1976), 294–312. MR 415366, DOI 10.1515/crll.1976.283-284.294
- 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 Tehnica, 1987.
- M. S. Brodskiĭ, Triangular and Jordan representations of linear operators, Translations of Mathematical Monographs, Vol. 32, American Mathematical Society, Providence, R.I., 1971. Translated from the Russian by J. M. Danskin. MR 0322542
- Luminiţa Lemnete, An operator-valued moment problem, Proc. Amer. Math. Soc. 112 (1991), no. 4, 1023–1028. MR 1059628, DOI 10.1090/S0002-9939-1991-1059628-5
- Mihai Putinar, Inverse problems of perturbation theory and moment problems, Functional analysis & related topics (Sapporo, 1990) World Sci. Publ., River Edge, NJ, 1991, pp. 99–116. MR 1148610
- Palle E. T. Jorgensen, Existence of smooth solutions to the classical moment problems, Trans. Amer. Math. Soc. 332 (1992), no. 2, 839–848. MR 1059709, DOI 10.1090/S0002-9947-1992-1059709-1
Additional Information
- © Copyright 1995 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 123 (1995), 747-754
- MSC: Primary 47A57
- DOI: https://doi.org/10.1090/S0002-9939-1995-1223267-7
- MathSciNet review: 1223267