Geodesic
POSITIVE DEFINITE FUNCTIONS AND SEBESTYÉN'S OPERATOR MOMENT PROBLEM
Glasgow mathematical journal, Tome 47 (2005) no. 3, pp. 471-488

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DOI

Given a sequence $\{A_n\}_{n\in\mathbb{Z}_+}$ of bounded linear operators between complex Hilbert spaces $\mathcal{H}$ and $\mathcal{K}$ we characterize the existence of a contraction (resp. isometry, unitary operator, shift) $T$ on $\mathcal{K}$ such that \[A_n=T^nA_0,\quad n\in\mathbb{Z}_+.\] Such moment problems are motivated by their connection with the dilatability of positive operator measures having applications in the theory of stochastic processes.The solutions, based on the fact that a certain operator function attached to $T$ is positive definite on $\mathbb{Z}$, extend the ones given by Sebestyén in [18], [19] or, recently, by Jabłoński and Stochel in [8]. Some applications, containing new characterizations for isometric, unitary operators, orthogonal projections or commuting pairs having regular dilation, conclude the paper.
DOI : 10.1017/S0017089505002715
Mots-clés : Primary 47A57, 43A35, Secondary 47A20, 60G10, 47B99 
SEBESTYÉN, ZOLTÁN; POPOVICI, DAN. POSITIVE DEFINITE FUNCTIONS AND SEBESTYÉN'S OPERATOR MOMENT PROBLEM. Glasgow mathematical journal, Tome 47 (2005) no. 3, pp. 471-488. doi: 10.1017/S0017089505002715
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     title = {POSITIVE {DEFINITE} {FUNCTIONS} {AND} {SEBESTY\'EN'S} {OPERATOR} {MOMENT} {PROBLEM}},
     journal = {Glasgow mathematical journal},
     pages = {471--488},
     year = {2005},
     volume = {47},
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     doi = {10.1017/S0017089505002715},
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