论文标题
在一些特殊的Banach空间上的运营商数字范围
On the numerical range of operators on some special Banach spaces
论文作者
论文摘要
复杂的Banach空间上有界线性运算符的数值范围不必与希尔伯特空间不同。本文的目的是在$ \ ell^2_p $上研究运营商$ t $，数值范围为凸。 We also obtain a nice relation between $V(T)$ and $ V(T^t)$ considering $ T \in \mathbb{L} (\ell_p^2) $ and $ T^t \in \mathbb{L} (\ell_q^2) ,$ where $T^t$ denotes the transpose of $T$ and $p$ and $q$ are conjugate real numbers i.e., $ 1 <p，q <\ infty $和$ \ frac {1} {p}+\ frac {1} {q} =1。$
The numerical range of a bounded linear operator on a complex Banach space need not be convex unlike that on a Hilbert space. The aim of this paper is to study operators $T$ on $ \ell^2_p $ for which the numerical range is convex. We also obtain a nice relation between $V(T)$ and $ V(T^t)$ considering $ T \in \mathbb{L} (\ell_p^2) $ and $ T^t \in \mathbb{L} (\ell_q^2) ,$ where $T^t$ denotes the transpose of $T$ and $p$ and $q$ are conjugate real numbers i.e., $ 1 <p,q< \infty $ and $ \frac{1}{p}+\frac{1}{q}=1.$
