On the $A$-$q$-Numerical Range of Operators in Semi-Hilbertian Spaces
Functional Analysis
2025-11-11 v2
Abstract
This study investigates the --numerical range of an operator within the framework of semi-Hilbertian spaces. Several fundamental properties of the --numerical range are established, including spectral inclusion results and a disk union formula. Bounds for the --numerical radius are derived, extending and generalizing previously known results. Finally, the notion of -nilpotent operator is introduced, and it is shown that the --numerical range of an -nilpotent operator with index is a disk (open or closed) in the complex plane.
Keywords
Cite
@article{arxiv.2502.19855,
title = {On the $A$-$q$-Numerical Range of Operators in Semi-Hilbertian Spaces},
author = {Jyoti Rani and Arnab Patra and Riddhick Birbonshi},
journal= {arXiv preprint arXiv:2502.19855},
year = {2025}
}