PreprintCC BY 4.0arXiv
Convex-cyclic and super convex-cyclic weighted shifts
Abstract
Convex-cyclic operators are considered by H. Rezaei \cite{R1}. However, there is a general lack of theoretical understanding of super convex-cyclic operators. In this paper, we analyze super convex-cyclic operators. In particular, Super Convex-cyclicity Criterion is described. Additionally, we characterize convex-cyclicity of (invertible) bilateral weighted shifts in terms of their weight sequences, which in turn correct \cite[H. Rezaei (2013) Theorem 4.2 ]{R1}. Meanwhile, we give super convex-cyclicity of (invertible) weighted shifts in the bilateral case.
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BibTeX
@misc{wang2026convexcyclic,
title = {{Convex-cyclic and super convex-cyclic weighted shifts}},
author = {Cui Wang and Ze-Hua Zhou},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.26978},
eprint = {2610.26978},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.26978},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Convex-cyclic and super convex-cyclic weighted shifts
AU - Cui Wang
AU - Ze-Hua Zhou
PY - 2026
DA - 2026/10/19
PB - arXiv
DO - 10.48550/arxiv.2610.26978
UR - https://arxiv.org/abs/2610.26978
AB - Convex-cyclic operators are considered by H. Rezaei \cite{R1}. However, there is a general lack of theoretical understanding of super convex-cyclic operators. In this paper, we analyze super convex-cyclic operators. In particular, Super Convex-cyclicity Criterion is described. Additionally, we characterize convex-cyclicity of (invertible) bilateral weighted shifts in terms of their weight sequences, which in turn correct \cite[H. Rezaei (2013) Theorem 4.2 ]{R1}. Meanwhile, we give super convex-cyclicity of (invertible) weighted shifts in the bilateral case.
ER -