论文标题
关于有限线性操作员的正交性的一些评论
Some remarks on orthogonality of bounded linear operators
论文作者
论文摘要
我们探讨了在操作员空间和地面空间中元素的正交性之间的正交性之间的关系。确切地说，我们研究如果$ t，a \ in \ mathbb {l}（\ mathbb {x}，\ mathbb {y}）$满足$ t \ bot_b a，$，那么是否存在$ x \ in \ mathbb {x} $ tx \ bot_b ax_b ax $ $ x $ = 1，\ | tx \ | = \ | t \ | $，其中$ \ mathbb {x}，\ mathbb {y} $是标准的线性空间。 在这种情况下，我们介绍了Banach空间的属性$ P_N $的概念，并说明了其与Banach空间之间有界线性运算符的正交性的联系。我们进一步研究属性$ p_n $，用于各种多面体Banach空间。
We explore the relation between the orthogonality of bounded linear operators in the space of operators and that of elements in the ground space. To be precise, we study if $ T, A \in \mathbb{L}(\mathbb{X}, \mathbb{Y}) $ satisfy $ T \bot_B A,$ then whether there exists $ x \in \mathbb{X} $ such that $ Tx\bot_B Ax$ with $ \|x\| =1, \|Tx\| = \|T\|$, where $\mathbb{X}, \mathbb{Y} $ are normed linear spaces. In this context, we introduce the notion of Property $ P_n $ for a Banach space and illustrate its connection with orthogonality of a bounded linear operator between Banach spaces. We further study Property $ P_n $ for various polyhedral Banach spaces.
