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PreprintarXiv licencearXiv

Property (R) with its stability for analytic functional system and under compact perturbations

  • Sinan Qiu
  • Lining Jiang
  • Xiaomin Wei
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Abstract

Let ℱT be the analytic functional system generated by a linear bounded operator T on an infinite dimensional complex Hilbert space. This paper characterizes the stability of property (R), a variant of Weyl's theorem, for ℱT and under compact perturbations in terms of the spectrum on consistency in Weyl. In particular, the stability of property (R) under compact perturbations is shown to imply the (R)-stability of ℱT.

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Cite

BibTeXRIS
BibTeX
@misc{qiu2026property,
  title = {{Property (R) with its stability for analytic functional system and under compact perturbations}},
  author = {Sinan Qiu and Lining Jiang and Xiaomin Wei},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.29710},
  eprint = {2610.29710},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.29710},
}
RIS
TY  - UNPB
TI  - Property (R) with its stability for analytic functional system and under compact perturbations
AU  - Sinan Qiu
AU  - Lining Jiang
AU  - Xiaomin Wei
PY  - 2026
DA  - 2026/10/21
PB  - arXiv
DO  - 10.48550/arxiv.2610.29710
UR  - https://arxiv.org/abs/2610.29710
AB  - Let ℱ_T be the analytic functional system generated by a linear bounded operator T on an infinite dimensional complex Hilbert space. This paper characterizes the stability of property (R), a variant of Weyl's theorem, for ℱ_T and under compact perturbations in terms of the spectrum on consistency in Weyl. In particular, the stability of property (R) under compact perturbations is shown to imply the (R)-stability of ℱ_T.
ER  -