论文标题
运营商满足某些形式的主教 - 玻璃体类型属性和数值半径
Operators satisfying some forms of Bishop-Phelps-Bollobas type properties for norm and numerical radius
论文作者
论文摘要
在本文中，我们研究了属性的较弱形式$ \ text {\ textbf {l}} _ {o，o} $称为弱$ \ text {\ textbf {l textbf {l}} _ {o，o，o} $及其统一版本及其统一版本，称为弱$ \ text {bpb} proplo $ \ text {bpb} _ {\ text {op}} $用于一对巴拉克空间。我们证明，当且仅当$（x，x，\ mathbb {r}）$中，banach space $ x $具有反射性且均匀均匀的凸，才有属性弱$ \ text {bpb} _ {\ text {op text {op}} $。我们进一步研究了所有有界线性运算符的类，从BANACH空间到另一个满足属性的Banach空间，这些属性弱$ \ text {\ textbf {l}} _ {o，o，o} $。最后，我们介绍并研究了有界线性图的数值半径的相似特性。
In this paper we study a weaker form of the property $\text{\textbf{L}}_{o,o}$ called the weak $\text{\textbf{L}}_{o,o}$ and its uniform version called the weak $\text{BPB}_{\text{op}}$ which is again a weaker form the property $\text{BPB}_{\text{op}}$ for a pair of Banach spaces. We prove that a Banach space $X$ is reflexive and weakly uniformly convex if and only if the pair $(X,\mathbb{R})$ has the property weak $\text{BPB}_{\text{op}}$. We further investigate the class of all bounded linear operators from a Banach space to another Banach space satisfying the property weak $\text{\textbf{L}}_{o,o}$. Finally we introduce and study similar properties for numerical radius of a bounded linear map.
