Sebestyén moment problem: The multi-dimensional case
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- by Dan Popovici and Zoltán Sebestyén
- Proc. Amer. Math. Soc. 132 (2004), 1029-1035
- DOI: https://doi.org/10.1090/S0002-9939-03-07291-5
- Published electronically: December 1, 2003
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Abstract:
Given a family $\{h_{\mathbf {n}}\}_{\mathbf {n}\in \mathbb {Z}_+^\Omega }$ of vectors in a Hilbert space $\mathcal {H}$ we characterize the existence of a family of commuting contractions $\mathbf {T}=\{T_\omega \}_{w\in \Omega }$ on $\mathcal {H}$ having regular dilation and such that \begin{equation*} h_{\mathbf {n}}=\mathbf {T} ^{\mathbf {n}} h_{\mathbf {0}},\quad \mathbf {n}\in \mathbb {Z}_+^\Omega . \end{equation*} The theorem is a multi-dimensional analogue for some well-known operator moment problems due to Sebestyén in case $|\Omega |=1$ or, recently, to Găvruţă and Păunescu in case $|\Omega |=2$.References
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Bibliographic Information
- Dan Popovici
- Affiliation: Department of Mathematics, University of the West, Ro-1900 Timişoara, Bd. V. Pârvan 4, Romania
- Email: popovici@math.uvt.ro
- Zoltán Sebestyén
- Affiliation: Department of Applied Analysis Loránd Eötvös University, H-1117 Budapest, Pázmány Péter sétány 1/C, Hungary
- Email: sebesty@cs.elte.hu
- Received by editor(s): October 22, 2002
- Published electronically: December 1, 2003
- Communicated by: Joseph A. Ball
- © Copyright 2003 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 132 (2004), 1029-1035
- MSC (2000): Primary 47A57, 47A20
- DOI: https://doi.org/10.1090/S0002-9939-03-07291-5
- MathSciNet review: 2045418
Dedicated: To the memory of Gyula Farkas