Year: 2026
Type: preprint
Abstract: We introduce two James-type constants associated with approximate isosceles and approximate Birkhoff--James orthogonality in real normed spaces. The isosceles family coincides with the classical James constant of Gao and Lau [J. Austral. Math. Soc. Ser. A 48 (1990), 101--112], while the Birkhoff family extends the orthogonal James constant of Baronti and Papini [Constr. Math. Anal. 5 (2022), no.~1, 37--45]. We show that approximate orthogonality constraints can, in certain settings, recover classical geometric constants exactly. In particular, the approximate isosceles family collapses to the classical James constant, while the approximate Birkhoff--James family forms a genuine parameter-dependent interpolation between the orthogonal and classical James constants.We also compare the Birkhoff profile with several classical geometric constants and study how it changes with the parameter.Several examples are also given to illustrate the relation between geometric constants and approximate orthogonality.
Source: arXiv (Cornell 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: W7214953263