Year: 2026
Type: preprint
Abstract: We provide a strengthened answer to the questions posed by Alonso, Martín, and Papini [Studia Math. 188 (2008), 135--150] concerning the comparison between the von Neumann--Jordan and James constants . The classical inequality $\CNJ(X)\leq J(X)$ between the von Neumann--Jordan and James constants was established by Takahashi and Kato [J. Math. Anal. Appl. 359 (2009), 602--609], Wang [Proc. Amer. Math. Soc. 138 (2010), 695--701], and Yang and Li [Appl. Math. Lett. 23 (2010), 277--281], while related sharp estimates were obtained by Kato and Takahashi [Rend. Circ. Mat. Palermo (2) Suppl. 82 (2010), 75--91]. We sharpen this inequality to $\CNJ(X)\leq\JB(X)$, where $\JB(X)$ is the Birkhoff--James orthogonal James constant introduced by Baronti and Papini [Constr. Math. Anal. 5 (2022), 37--45]. Our proof employs optimal distance ellipses and alternating contact directions.
Source: arXiv (Cornell University)
Authors: Fang, Zhiyao, Liu, Qi
Institution: Anqing Normal University
Language: English
Topic: Advanced Banach Space Theory
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funders: Strong, Anqing Normal University
OpenAlex ID: W7221572867