论文标题
在$ a $ - 平行式和$ a $ -birkhoff-james的正交性
On $A$-parallelism and $A$-Birkhoff-James orthogonality of operators
论文作者
论文摘要
在本文中，我们建立了$ A $ A $平行性线性运算符的$ A $平行性，相对于在复杂的Hilbert Space上作用的正运算符$ a $引起的eminorm。除其他事项外，我们研究了$ -seminorm-parallelisl和$ -Birkhoff-James的正交性之间的关系。特别是，我们表征了$ a $ and的运营商，这些运营商满足$ a $ -daugavet方程。此外，我们将运营商和距离公式的$ a $ -birkhoff-james正交性联系起来，并以$ a的运营商提供了中心质量的明确公式。还讨论了其他一些相关的结果。
In this paper, we establish several characterizations of the $A$-parallelism of bounded linear operators with respect to the seminorm induced by a positive operator $A$ acting on a complex Hilbert space. Among other things, we investigate the relationship between $A$-seminorm-parallelism and $A$-Birkhoff-James orthogonality of $A$-bounded operators. In particular, we characterize $A$-bounded operators which satisfy the $A$-Daugavet equation. In addition, we relate the $A$-Birkhoff-James orthogonality of operators and distance formulas and we give an explicit formula of the center mass for $A$-bounded operators. Some other related results are also discussed.
