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

@misc{majumdar2026some,
  title = {{Some Generalized Numerical Ranges of Real-linear Operators on Hilbert Spaces}},
  author = {Arup Majumdar and Vladimir Muller},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.16823},
  eprint = {2610.16823},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.16823},
  note = {CC BY-NC-SA 4.0},
}

TY  - UNPB
TI  - Some Generalized Numerical Ranges of Real-linear Operators on Hilbert Spaces
AU  - Arup Majumdar
AU  - Vladimir Muller
PY  - 2026
DA  - 2026/10/12
PB  - arXiv
DO  - 10.48550/arxiv.2610.16823
UR  - https://arxiv.org/abs/2610.16823
AB  - 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.
ER  -