Convex-Cyclic Weighted Translations On Locally Compact Groups

2022/11/03 by M. R. Azimi, Azimi, M. R., I. Akbarbaglu +3
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #Functional Analysis (math.FA) #Nonlinear Differential Equations Analysis #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2211.01623

openalex publication_date 2022/11/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A bounded linear operator T on a Banach space X is called a convex-cyclic operator if there exists a vector x ∈ 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 ↦ w⋅ f*δ_g on \mathfrakL^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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