.png){kind=icon}
.png){kind=icon}
Return
The Kaczmarz Algorithm in Hilbert C*-modules
.png){kind=icon}
OA
AI
DOI：10.1016/j.exmath.2025.125738.png)
.png){kind=icon}
.png){kind=icon}
Share.png){kind=icon}
Save
Abstract
En 中文
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. (c) 2025 The Author(s). Published by Elsevier GmbH. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
Keywords:
Kaczmarz algorithm
Hilbert C* modules
Orbits of bounded operators
AI Summary
Key information extracted from the uploaded paper, including a brief overview, abstract, background, key highlights, visual analysis, and future outlook.
Journal
E
IF:
0.9
Papers:
43
Citations:
0
View more organizations