论文标题
局部紧凑型组的凸循环加权翻译
Convex-Cyclic Weighted Translations On Locally Compact Groups
论文作者
论文摘要
如果存在x $的vector $ x \，则banach space $ x $上有界的线性运算符$ t $，称为convex-cyclic运算符，以使$ orb的凸壳（t，x）$在$ x $中密集。在本文中，对于本地紧凑的组$ g $，对于给定的基于基本元素$ g $，我们为加权翻译运算符$ t_ {g，w}提供了一些足够条件：f \ mapsto w \ cdot w \ cdcdΔ_g$ on $ \ \ \ \ \ \ \ \ m mathfrak {l}^p}^p}^{p}（g）$还研究了必要的条件。最后，为解释获得的结果，给出了一些示例。
A bounded linear operator $T$ on a Banach space $X$ is called a convex-cyclic operator if there exists a vector $x \in X$ such that the convex hull of $Orb(T, x)$ is dense in $X$. In this paper, for given an aperiodic element $g$ in a locally compact group $G$, we give some sufficient conditions for a weighted translation operator $T_{g,w}: f \mapsto w\cdot f*δ_g$ on $\mathfrak{L}^{p}(G)$ to be convex-cyclic. A necessary condition is also studied. At the end, to explain the obtained results, some examples are given.
