Preprint
The Local Operator Moment Problem on ℝ
ArXiv.org
Cornell University
05/06/2026
DOI: 10.48550/arxiv.2605.04392
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.
Details
- Title: Subtitle
- The Local Operator Moment Problem on ℝ
- Creators
- Raul E CurtoAbderrazzak Ech-charyfyHamza El AzharEl Hassan Zerouali
- Resource Type
- Preprint
- Publication Details
- ArXiv.org
- DOI
- 10.48550/arxiv.2605.04392
- ISSN
- 2331-8422
- Publisher
- Cornell University; Ithaca, New York
- Language
- English
- Date posted
- 05/06/2026
- Academic Unit
- Mathematics
- Record Identifier
- 9985161447902771
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