论文标题
Birkhoff-James的正交性及其在某些功能空间中的点对称性
Birkhoff-James Orthogonality and Its Pointwise Symmetry in Some Function Spaces
论文作者
论文摘要
我们研究了Birkhoff-James正交性及其在交换性$ C^*$代数中的尖端对称性，即，在Infinity消失的本地紧凑型Hausdorff空间上定义的所有连续函数的空间。我们使用此表征来获得Birkhoff-James正交性在$ L_ \ Infty $空间上定义在任何任意度量空间上的表征。我们还以$ 1 \ leq p <\ infty $的价格为$ l_p $ spaces做同样的事情。
We study Birkhoff-James orthogonality and its pointwise symmetry in commutative $C^*$ algebras, i.e., the space of all continuous functions defined on a locally compact Hausdorff space that vanish at infinity. We use this characterization to obtain the characterization of Birkhoff-James orthogonality on $L_\infty$ space defined on any arbitrary measure space. We also do the same for the $L_p$ spaces for $1\leq p<\infty$.
