论文标题
在规范线性空间中Birkhoff-James正交性的局部近似对称性
Local approximate symmetry of Birkhoff-James orthogonality in normed linear spaces
论文作者
论文摘要
Dragomir和Chmie \-liń\ -ski引入了两个不同的birkhoff-james正交性的近似birkhoff-james正交性。在本文中，我们考虑了Birkhoff-James正交性的全球和局部近似对称性与两个定义相关。我们证明，在所有有限维的BANACH空间中，在Dragomir的意义上，所考虑的正交性近似对称。对于另一种情况，我们证明，对于有限的多面性巴拉赫空间，正交性的近似对称性等同于一些新引入的几何特性。我们的调查补充并扩展了有关伯克霍夫詹姆斯正交性的全球近似对称性的一些最新结果的范围。
Two different notions of approximate Birkhoff-James orthogonality in nor\-med linear spaces have been introduced by Dragomir and Chmie\-liń\-ski. In the present paper we consider a global and a local approximate symmetry of the Birkhoff-James orthogonality related to each of the two definitions. We prove that the considered orthogonality is approximately symmetric in the sense of Dragomir in all finite-dimensional Banach spaces. For the other case, we prove that for finite-dimensional polyhedral Banach spaces, the approximate symmetry of the orthogonality is equivalent to some newly introduced geometric property. Our investigations complement and extend the scope of some recent results on a global approximate symmetry of the Birkhoff-James orthogonality.
