2025/08/19 by Alpay, Daniel, Berner, Chad, Weber, Eric S.
#41A65 #46L08 (Primary) 42C15 (Secondary) #FOS: Mathematics #Functional Analysis (math.FA)
paper · doi:10.48550/arxiv.2508.13861
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.