发表机构
School of Mathematics and Statistics, Anqing Normal University; School of Mathematics and Statistics, Guangdong University of Foreign Studies; Department of Mathematics, Sun Yat-sen University（安庆师范大学数学与统计学院; 广东外语外贸大学数学与统计学院; 中山大学数学系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文在实赋范空间中引入两类与近似正交性相关的James型常数，证明近似等腰族退化为经典James常数，而近似Birkhoff族形成参数依赖插值，并比较其与经典几何常数的关系。
AI 中文摘要
我们在实赋范空间中引入了与近似等腰性和近似Birkhoff--James正交性相关的两个James型常数。等腰族与Gao和Lau [J. Austral. Math. Soc. Ser. A 48 (1990), 101--112]的经典James常数一致，而Birkhoff族则扩展了Baronti和Papini [Constr. Math. Anal. 5 (2022), no.~1, 37--45]的正交James常数。我们证明了在某些设定下，近似正交约束能够精确地恢复经典几何常数。特别地，近似等腰族退化为经典James常数，而近似Birkhoff--James族则构成了正交James常数与经典James常数之间真正的参数依赖插值。我们还比较了Birkhoff轮廓与若干经典几何常数，并研究了其随参数的变化情况。文中还给出了具体例子，以说明几何常数与近似正交性之间的关系。
英文摘要
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.
