A solution to a conjecture on the norm of the Copson operator minus the Identity for monotone sequences
Year: 2026
Type: preprint
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 $\ell^p(\mathbb{N})$. 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).
Source: arXiv (Cornell University)
Authors: Said, Achraf Ben, Gogatishvili, Amiran
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: G1741043573, G597650774
OpenAlex ID: W7214001725