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Examples of Noncompact Quasinilpotent Hankel Operators
Abstract
For every nonzero real number a, we prove that the integral Hankel operator on L2(ℝ+) with kernel k(t)=t−1+ia is noncompact quasinilpotent. This answers in the affirmative a question by Peller \cite{Peller1998} about the existence of noncompact quasinilpotent Hankel operators. Moreover, we obtain the corresponding Hankel operators on the Hardy space with symbols ((1−z)/(1+z))ia.
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BibTeX
@misc{sang2026examples,
title = {{Examples of Noncompact Quasinilpotent Hankel Operators}},
author = {Yuanqi Sang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.25184},
eprint = {2609.25184},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.25184},
}
RIS
TY - UNPB
TI - Examples of Noncompact Quasinilpotent Hankel Operators
AU - Yuanqi Sang
PY - 2026
DA - 2026/09/21
PB - arXiv
DO - 10.48550/arxiv.2609.25184
UR - https://arxiv.org/abs/2609.25184
AB - For every nonzero real number a, we prove that the integral Hankel operator on L^2(ℝ_+) with kernel k(t)=t^−1+ia is noncompact quasinilpotent. This answers in the affirmative a question by Peller \cite{Peller1998} about the existence of noncompact quasinilpotent Hankel operators. Moreover, we obtain the corresponding Hankel operators on the Hardy space with symbols ((1−z)/(1+z))^ia.
ER -