Year: 2026
Type: preprint
Abstract: This paper introduces and systematically investigates several classes of numerical ranges associated with real-linear operators on Hilbert spaces, including the essential numerical range, maximal numerical range, essential maximal numerical range, $q$-numerical range, and trace numerical range. We establish fundamental structural properties of these sets and characterize their geometric shape. In particular, we analyze how the real-linear nature of the operators influences the geometry and spectral behaviour of the corresponding numerical ranges, thereby extending and enriching the theory of numerical ranges from complex-linear to real-linear operator settings.
Source: arXiv (Cornell University)
Authors: Majumdar, Arup, Muller, Vladimir
Language: English
Topic: Advanced Banach Space Theory
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Award: G3063752827
OpenAlex ID: W7221785872