2018/10/09 by Marko S. Djikić, Djikić, Marko S., Jovana Nikolov Radenković +1
Computer Science · Mathematics · #46C07 #47A20 #Advanced Topics in Algebra #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Matrix Theory and Algorithms
paper · pdf · doi:10.48550/arxiv.1810.04062
openalex publication_date 2018/10/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The paper is concerned with the following question: if A and B are two bounded operators between Hilbert spaces H and K, and M and N are two closed subspaces in H, when will there exist a bounded operator C:H\toK which coincides with A on M and with B on N simultaneously? Besides answering this and some related questions, we also wish to emphasize the role played by the class of so-called semiclosed operators and the unbounded Moore-Penrose inverse in this work. Finally, we will relate our results to several well-known concepts, such as the operator equation XA=B and the theorem of Douglas, Halmos' two projections theorem, and Drazin's star partial order.