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The Local Operator Moment Problem on ℝ
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The Local Operator Moment Problem on ℝ

Raul E Curto, Abderrazzak Ech-charyfy, Hamza El Azhar and El Hassan Zerouali
ArXiv.org
Cornell University
05/06/2026
DOI: 10.48550/arxiv.2605.04392
url
https://doi.org/10.48550/arxiv.2605.04392View
Preprint (Author's original) This preprint has not been evaluated by subject experts through peer review. Preprints may undergo extensive changes and/or become peer-reviewed journal articles. Open Access

Abstract

We study the connections between operator moment sequences T = (Tn)n∈Z+ of self-adjoint operators on a complex Hilbert space H and the local moment sequences ⟨T x, x⟩ = (⟨Tnx, x⟩)n∈Z+ for arbitrary x ∈ H. We provide necessary and sufficient conditions for solving the operator moment problem on R, and we show that these criteria are au- tomatically valid on compact subsets of R. Applications of the compact case are used to study subnormal operator weighted shifts. A Stampfli- type propagation theorem for subnormal operator weighted shifts is also established. In addition, we discuss the validity of Tchakaloff’s Theo- rem for operator moment sequences with compact support. In the case of a recursively generated sequence of self-adjoint operators, necessary and sufficient conditions for an affirmative answer to the operator recur- sive moment problem are provided, and the support of the associated representing operator-valued measure is described.
Mathematics - Functional Analysis

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