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Numerical range and invariant subspaces of weighted composition operators on the Hardy space of Dirichlet series

  • Sudeshna Lahiri
  • Sarita Ojha
  • Subhadip Halder
  • Riddhick Birbonshi
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Abstract

In this paper, we study various results on numerical range of weighted composition operators on Hardy space of Dirichlet series. Certain conditions are provided under which the numerical range contains zero and some circular or elliptic disks. With the help of invariant subspaces of the operator, we also determine the numerical range of reductive weighted composition operators on this space. Additionally, we discuss some results on the Davis-Wielandt shell of composition operators with some natural questions that arise from our findings.

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Cite

BibTeXRIS
BibTeX
@misc{lahiri2026numerical,
  title = {{Numerical range and invariant subspaces of weighted composition operators on the Hardy space of Dirichlet series}},
  author = {Sudeshna Lahiri and Sarita Ojha and Subhadip Halder and Riddhick Birbonshi},
  howpublished = {arXiv},
  year = {2026},
  month = aug,
  doi = {10.48550/arxiv.2608.29294},
  eprint = {2608.29294},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.29294},
}
RIS
TY  - UNPB
TI  - Numerical range and invariant subspaces of weighted composition operators on the Hardy space of Dirichlet series
AU  - Sudeshna Lahiri
AU  - Sarita Ojha
AU  - Subhadip Halder
AU  - Riddhick Birbonshi
PY  - 2026
DA  - 2026/08/29
PB  - arXiv
DO  - 10.48550/arxiv.2608.29294
UR  - https://arxiv.org/abs/2608.29294
AB  - In this paper, we study various results on numerical range of weighted composition operators on Hardy space of Dirichlet series. Certain conditions are provided under which the numerical range contains zero and some circular or elliptic disks. With the help of invariant subspaces of the operator, we also determine the numerical range of reductive weighted composition operators on this space. Additionally, we discuss some results on the Davis-Wielandt shell of composition operators with some natural questions that arise from our findings.
ER  -