2023/12/15 by Cristian Conde, Conde, Cristian, Kais Feki +1
Computer Science · Decision Sciences · Mathematics · #46C05 #47A05 #47A12 #47B65 #47L05 #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Inequalities and Applications #Matrix Theory and Algorithms #Multi-Criteria Decision Making
paper · doi:10.48550/arxiv.2312.10135
openalex publication_date 2023/12/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper explores the concept of approximate Birkhoff-James orthogonality in the context of operators on semi-Hilbert spaces. These spaces are generated by positive semi-definite sesquilinear forms. We delve into the fundamental properties of this concept and provide several characterizations of it. Using innovative arguments, we extend a widely known result initially proposed by Magajna in [J. London. Math. Soc., 1993]. Additionally, we improve a recent result by Sen and Paul in [Math. Slovaca, 2023] regarding a characterization of approximate numerical radius orthogonality of two semi-Hilbert space operators, such that one of them is A-positive. Here, A is assumed to be a positive semi-definite operator.