Citation:
Makhlouf S, Lombarkia F. A New Generalization of Fuglede's Theorem and Operator Equations. Nonlinear Dynamics & Systems Theory [Internet]. 2024;24 (6) :603-614.
Abstract:
The article focuses on the generalization of Fuglede's theorem and the solvability of operator equations. Topics include extending Fuglede's theorem to non-normal operators, deriving criteria for solving operator equations such as AX − XB = C, and using inner inverses to establish necessary and sufficient conditions for operator equation solutions.