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Sebestyén moment problem: The multi-dimensional case


Authors: Dan Popovici and Zoltán Sebestyén
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
Published electronically: December 1, 2003
MathSciNet review: 2045418
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Abstract | References | Similar Articles | Additional Information

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 $|\Omega |=2$.


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Additional 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

Keywords: Sebestyén operator moment problem, multi-contraction, regular dilation, positive definite function
Received by editor(s): October 22, 2002
Published electronically: December 1, 2003
Dedicated: To the memory of Gyula Farkas
Communicated by: Joseph A. Ball
Article copyright: © Copyright 2003 American Mathematical Society