Proceedings of the American Mathematical Society

Author(s): Dan Popovici; Zoltán Sebestyén
Journal: Proc. Amer. Math. Soc. 132 (2004), 1029-1035.
MSC (2000): Primary 47A57, 47A20
Posted: 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

The theorem is a multi-dimensional analogue for some well-known operator moment problems due to Sebestyén in case $\vert\Omega\vert=1$ or, recently, to Gavruta and Paunescu in case $\vert\Omega\vert=2$ .

1.: S. Brehmer, Über vertauschbare Kontraktionen des Hilbertschen Raumes, Acta Sci. Math. Szeged 22 (1961), 106-111. MR 24:A1023a
2.: P. Gavruta and D. Paunescu, Sebestyén's moment problem and regular dilations, Acta Math. Hungar. 94 (2002), 223-232. MR 2003g:47014
3.: I. Halperin, Sz.-Nagy - Brehmer dilations, Acta Sci. Math. Szeged 23 (1962), 279-289. MR 27:6127a
4.: M. A. Neumark, Positive definite operator functions on a commutative group, Bulletin Acad. Sci. URSS Sér. Math. 7 (1943), 237-244. MR 5:272c
5.: Z. Sebestyén, Moment theorems for operators on Hilbert space, Acta Sci. Math. Szeged 44 (1982), 165-171. MR 84f:47004
6.: B. Sz.-Nagy, Bemerkungen zur vorstehenden Arbeit des Herrn S. Brehmer, Acta Sci. Math. Szeged 22 (1961), 112-114. MR 24:A1023b
7.: B. Sz.-Nagy and C. Foias, Harmonic analysis of operators on Hilbert space, Akadémiai Kiadó, Budapest, North-Holland, Amsterdam, London, 1970. MR 43:947

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 47A57, 47A20

Dan Popovici
Affiliation: Department of Mathematics, University of the West, Ro-1900 Timisoara, 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

DOI: 10.1090/S0002-9939-03-07291-5
PII: S 0002-9939(03)07291-5
Keywords: Sebesty\'en operator moment problem, multi-contraction, regular dilation, positive definite function
Received by editor(s): October 22, 2002
Posted: December 1, 2003
Dedicated: To the memory of Gyula Farkas
Communicated by: Joseph A. Ball
Copyright of article: Copyright 2003, American Mathematical Society

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