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arXiv · 2211.01623

Convex-Cyclic Weighted Translations On Locally Compact Groups

M. R. Azimi·I. Akbarbaglu·M. Asadipour
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Abstract

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.

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M. R. Azimi, I. Akbarbaglu, M. Asadipour. 2022-11-03. Convex-Cyclic Weighted Translations On Locally Compact Groups. https://arxiv.org/abs/2211.01623

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