论文标题
Bishop-phelps-Bollobás型的本地形式，用于双线性地图
Local forms of Bishop-Phelps-Bollobás type properties for bilinear maps
论文作者
论文摘要
在本文中，我们表征了所谓的属性$ \ textbf {l} _ {o，o} $，由丹塔斯（Dantas）和鲁德（Rueda Zoca）定义，用于紧凑，虚弱的连续双线性地图。由此，我们通过定义弱$ \ textbf {l} _ {o，o} $来削弱此属性。我们提供了$ \ textbf {l} _ {o，o} $属性的等效性（x \ hat {\ otimes}_πy，\ mathbb {r}）$ for Linear函数和$（x，x，x，y;; \ alsbb {r}）$ for BiLinear y y y y $ y y y y y y y y y y y y y y y y y y y y y y $此外，我们还确定，在某些预先签约的条件下，如果bilnear映射$ t $属于满足属性$ \ textbf {l} _ {o，o} $（weff $ \ $ \ textbf {l textbf {l textbf {l} _ {l} _ {o，o，o} $）的$ bilinear map a thy thy thy thy thy的属性，则是A $ \ textbf {l} _ {o，o} $（resp。
In this paper, we characterize the so called property $\textbf{L}_{o,o}$ as defined by Dantas and Rueda Zoca, for compact, weak-weak continuous bilinear maps. Motivated by this we weaken this property by defining the weak $\textbf{L}_{o,o}$ for bilinear maps. We provide equivalence of the weak $\textbf{L}_{o,o}$ property of $(X\hat{\otimes}_πY,\mathbb{R})$ for linear functionals and that of $(X,Y;\mathbb{R})$ for bilinear forms under certain conditions on $X$ and $Y$. Moreover, we have also established that under certain preassigned conditions, if a bilnear map $T$ belongs to a class which satisfies the property $\textbf{L}_{o,o}$ (resp. the weak $\textbf{L}_{o,o}$) for bilinear maps, then $T^*$ is a member of a class of operators which satisfy the property $\textbf{L}_{o,o}$ (resp. the weak $\textbf{L}_{o,o}$) for operators.
