论文标题
Birkhoff-James正交性和应用：一项调查
Birkhoff-James orthogonality and applications : A survey
论文作者
论文摘要
在过去的几十年中，Birkhoff-James正交性的概念已用于多种应用中。在本调查文章中，提到了某些BANACH空间中Birkhoff-James正交性的必要条件的已知结果。他们在研究规范空间的几何形状时的应用。提供了这种正交性的概念与GATEAUX衍生物与标准函数的细分集之间的联系。也可以使用Birkhoff-James正交性的特征来获得几个有趣的距离公式。最后，获得了一些新的结果。
In the last few decades, the concept of Birkhoff-James orthogonality has been used in several applications. In this survey article, the results known on the necessary and sufficient conditions for Birkhoff-James orthogonality in certain Banach spaces are mentioned. Their applications in studying the geometry of normed spaces are given. The connections between this concept of orthogonality, and the Gateaux derivative and the subdifferential set of the norm function are provided. Several interesting distance formulas can be obtained using the characterizations of Birkhoff-James orthogonality, which are also mentioned. In the end, some new results are obtained.
