论文标题
$ C_0 $ -SUM空间上的Bishop-Phelps-Bollobás财产
The Bishop-Phelps-Bollobás property on the space of $c_0$-sum
论文作者
论文摘要
本文的主要目的是在$ C_0 $ BANACH SPACES上研究Bishop-Phelps-Bollobás类型属性。除其他结果外，我们还表明，每当$ x $均匀地凸出，$ x $均（复杂）均匀的convex时，这对$（c_0（x），y）$都有bishop-phelps-bollobás属性（简而言之，bpbp）。我们还证明，每当$ x $均匀凸出且均匀平滑时，这对$（C_0（x），C_0（x））$具有双线性形式的BPBP。这些扩展了先前已知的结果，即每当$ y $均匀凸出时，$（c_0，y）$具有运营商的BPBP，而$（C_0，C_0）$具有双线性表单的BPBP。我们还可以在本地bpbp上获得一些结果，该结果称为$ \ mathbf {l} _ {p，p，p} $，用于运算符和双线性表单。
The main purpose of this paper is to study Bishop-Phelps-Bollobás type properties on $c_0$ sum of Banach spaces. Among other results, we show that the pair $(c_0(X),Y)$ has the Bishop-Phelps-Bollobás property (in short, BPBp) for operators whenever $X$ is uniformly convex and $Y$ is (complex) uniformly convex. We also prove that the pair $(c_0(X),c_0(X))$ has the BPBp for bilinear forms whenever $X$ is both uniformly convex and uniformly smooth. These extend the previously known results that $(c_0,Y)$ has the BPBp for operators whenever $Y$ is uniformly convex and $(c_0,c_0)$ has the BPBp for bilinear forms. We also obtain some results on a local BPBp which is called $\mathbf{L}_{p,p}$ for both operators and bilinear forms.
