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A solution to a conjecture on the norm of the Copson operator minus the Identity for monotone sequences
Abstract
We investigate the operator distance between the Identity and the Copson operator on the cone of nonnegative, nonincreasing sequences within the Lebesgue sequence spaces ℓp(ℕ). By proving the exact value of this distance, we confirm a conjecture originally formulated by A. Ben Said, S. Boza, and J. Soria in ``The norm of Hardy-type oscillation operators in the discrete and continuous settings'' (\emph{Analysis and Applications}, 2025).
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BibTeX
@misc{said2026solution,
title = {{A solution to a conjecture on the norm of the Copson operator minus the Identity for monotone sequences}},
author = {Achraf Ben Said and Amiran Gogatishvili},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.23035},
eprint = {2609.23035},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.23035},
}
RIS
TY - UNPB
TI - A solution to a conjecture on the norm of the Copson operator minus the Identity for monotone sequences
AU - Achraf Ben Said
AU - Amiran Gogatishvili
PY - 2026
DA - 2026/10/23
PB - arXiv
DO - 10.48550/arxiv.2609.23035
UR - https://arxiv.org/abs/2609.23035
AB - We investigate the operator distance between the Identity and the Copson operator on the cone of nonnegative, nonincreasing sequences within the Lebesgue sequence spaces ℓ^p(ℕ). By proving the exact value of this distance, we confirm a conjecture originally formulated by A. Ben Said, S. Boza, and J. Soria in ``The norm of Hardy-type oscillation operators in the discrete and continuous settings'' (\emph{Analysis and Applications}, 2025).
ER -