2024/11/23 by Sachin Manjunath Naik, Naik, Sachin Manjunath, P. Sam Johnson +1 · 1 citation
Computer Science · Engineering · Mathematics · #47A08 #47A58 #47A64 #47B65 #Aerospace Engineering and Control Systems #Approximation Theory and Sequence Spaces #FOS: Mathematics #Functional Analysis (math.FA) #Optimization and Variational Analysis
paper · pdf · doi:10.48550/arxiv.2411.15636
openalex publication_date 2024/11/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Complementable operators extend classical matrix decompositions, such as the Schur complement, to the setting of infinite-dimensional Hilbert spaces, thereby broadening their applicability in various mathematical and physical contexts. This paper focuses on the convergence properties of complementable operators, investigating when the limit of sequence of complementable operators remains complementable. We also explore the convergence of sequences and series of powers of complementable operators, providing new insights into their convergence behavior. Additionally, we examine the conditions under which the set of complementable operators is the subset of set of boundary points of the set of non-complementable operators with respect to the strong operator topology. The paper further explores the topological structure of the subset of complementable operators, offering a characterization of its closed subsets.