2025/02/27 by Rani, Jyoti, Patra, Arnab, Birbonshi, Riddhick
#46C05 (Primary) 15A60 #47A05 #47A12 (Secondary) #FOS: Mathematics #Functional Analysis (math.FA)
paper · doi:10.48550/arxiv.2502.19855
This study investigates the A-q-numerical range of an operator within the framework of semi-Hilbertian spaces. Several fundamental properties of the A-q-numerical range are established, including spectral inclusion results and a disk union formula. Bounds for the A-q-numerical radius are derived, extending and generalizing previously known results. Finally, the notion of A-nilpotent operator is introduced, and it is shown that the A-q-numerical range of an A-nilpotent operator with index 2 is a disk (open or closed) in the complex plane.