A solution to a conjecture on the norm of the Copson operator minus the Identity for monotone sequences

Achraf Ben Said; Amiran Gogatishvili

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arXiv · 2609.23035

A solution to a conjecture on the norm of the Copson operator minus the Identity for monotone sequences

Achraf Ben Said·Amiran Gogatishvili

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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).

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Achraf Ben Said, Amiran Gogatishvili. 2026-09-19. A solution to a conjecture on the norm of the Copson operator minus the Identity for monotone sequences. https://arxiv.org/abs/2609.23035

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