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arXiv · 2610.16823

Some Generalized Numerical Ranges of Real-linear Operators on Hilbert Spaces

Arup Majumdar·Vladimir Muller
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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.

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Arup Majumdar, Vladimir Muller. 2026-10-12. Some Generalized Numerical Ranges of Real-linear Operators on Hilbert Spaces. https://arxiv.org/abs/2610.16823

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