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PreprintCC0arXiv

Schatten class membership of products of composition operators and their adjoints

  • Qianrui Leng
  • Xianfeng Zhao
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Abstract

In this paper, we investigate the Schatten class membership of the product of a composition operator and the adjoint of another composition operator on the Hardy and Bergman spaces. We provide several sufficient conditions and necessary conditions for these operators to belong to the Schatten classes. Moreover, for some specific symbols including linear fractional maps, finite Blaschke products, and inner functions, we obtain necessary and sufficient conditions.

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Cite

BibTeXRIS
BibTeX
@misc{leng2026schatten,
  title = {{Schatten class membership of products of composition operators and their adjoints}},
  author = {Qianrui Leng and Xianfeng Zhao},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.15472},
  eprint = {2610.15472},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.15472},
  note = {CC0},
}
RIS
TY  - UNPB
TI  - Schatten class membership of products of composition operators and their adjoints
AU  - Qianrui Leng
AU  - Xianfeng Zhao
PY  - 2026
DA  - 2026/10/11
PB  - arXiv
DO  - 10.48550/arxiv.2610.15472
UR  - https://arxiv.org/abs/2610.15472
AB  - In this paper, we investigate the Schatten class membership of the product of a composition operator and the adjoint of another composition operator on the Hardy and Bergman spaces. We provide several sufficient conditions and necessary conditions for these operators to belong to the Schatten classes. Moreover, for some specific symbols including linear fractional maps, finite Blaschke products, and inner functions, we obtain necessary and sufficient conditions.
ER  -