Abstract
The Kaczmarz algorithm in Hilbert spaces is a classical iterative method for stably recovering vectors from inner product data. In this paper, we extend the algorithm to the setting of Hilbert C∗-modules and establish analogues of its effectiveness in both finite-dimensional and stationary cases. Consequently, we demonstrate that continuous families of elements in a Hilbert space can be uniformly recovered using the Kaczmarz algorithm. Additionally, we develop a normalized Cauchy transform for continuous families of measures and use it to provide sufficient conditions under which standard frames in Hilbert C(X)-modules can be generated by the Kaczmarz algorithm and realized as orbits of bounded operators.
Recommended Citation
D. Alpay et al., "The Kaczmarz Algorithm in Hilbert C∗-modules," Expositiones Mathematicae, vol. 44, no. 2, article no. 125738, Elsevier, Apr 2026.
The definitive version is available at https://doi.org/10.1016/j.exmath.2025.125738
Department(s)
Mathematics and Statistics
Publication Status
Open Access
Keywords and Phrases
Hilbert C* modules; Kaczmarz algorithm; Orbits of bounded operators
International Standard Serial Number (ISSN)
0723-0869
Document Type
Article - Journal
Document Version
Citation
File Type
text
Language(s)
English
Rights
© 2026 Elsevier, All rights reserved.
Creative Commons Licensing
This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License.
Publication Date
01 Apr 2026
