Some study of the approximate Birkhoff orthogonality and orthogonality of bounded linear operators
Some study of the approximate Birkhoff orthogonality and orthogonality of bounded linear operators
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DOI：
10.1007/s00010-023-00990-x
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发表时间：
2023-09
影响因子：
0.8
通讯作者：
Huayou Xie;Chuanjiang Zhou;Yongjin Li
中科院分区：
文献类型：
--
作者：
Huayou Xie;Chuanjiang Zhou;Yongjin Li
本文主要研究正交性，包括Birkhoff正交性、等腰正交性、勾股正交性和近似Birkhoff正交性。首先，利用近似Birkhoff正交性证明了线性泛函与超平面之间的关系。其次，我们建立了Birkhoff正交性和近似Birkhoff正交性的充分条件。给出了有界算子的等腰正交性和勾股正交性的一些充要条件。此外，我们还用函数正交性刻画了内积空间。
In this note, we are mainly interested in orthogonality, including Birkhoff orthogonality, isosceles orthogonality, Pythagorean orthogonality and approximate Birkhoff orthogonality. First, we show the relation between linear functionals and hyperplanes by means of approximate Birkhoff orthogonality. Second, we establish the sufficient conditions for Birkhoff orthogonality and approximate Birkhoff orthogonality. Then some sufficient and necessary conditions for isosceles orthogonality and Pythagorean orthogonality of bounded operators are shown. In addition, we characterize the inner product space in terms of functional orthogonality.