This paper investigates the scenario where two operators share the same range, which has proven to be highly beneficial in practical applications, especially for efficiently computing the Moore-Penrose inverse of specific operators. We establish specific conditions under which the reverse order law holds for Moore-Penrose inverses. Furthermore, we explore the relationship between the ranges and Moore-Penrose inverse of operators involved in a factorization $A = BDC$ within the framework of a Hilbert $C^*$-module.
Mohammadzadeh Karizaki,M. (2024). Operator range sharing and reverse order law for Moore-Penrose inverse in Hilbert $C^*$-modules. Journal of Frame and Matrix Theory, 1(2), 49-59. doi: 10.22034/jfmt.2024.458013.1012
MLA
Mohammadzadeh Karizaki,M. . "Operator range sharing and reverse order law for Moore-Penrose inverse in Hilbert $C^*$-modules", Journal of Frame and Matrix Theory, 1, 2, 2024, 49-59. doi: 10.22034/jfmt.2024.458013.1012
HARVARD
Mohammadzadeh Karizaki M. (2024). 'Operator range sharing and reverse order law for Moore-Penrose inverse in Hilbert $C^*$-modules', Journal of Frame and Matrix Theory, 1(2), pp. 49-59. doi: 10.22034/jfmt.2024.458013.1012
CHICAGO
M. Mohammadzadeh Karizaki, "Operator range sharing and reverse order law for Moore-Penrose inverse in Hilbert $C^*$-modules," Journal of Frame and Matrix Theory, 1 2 (2024): 49-59, doi: 10.22034/jfmt.2024.458013.1012
VANCOUVER
Mohammadzadeh Karizaki M. Operator range sharing and reverse order law for Moore-Penrose inverse in Hilbert $C^*$-modules. JFMT, 2024; 1(2): 49-59. doi: 10.22034/jfmt.2024.458013.1012
