Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
134 tokens/sec
GPT-4o
10 tokens/sec
Gemini 2.5 Pro Pro
47 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

A study of Bishop operators from the point of view of linear dynamics (2207.11419v1)

Published 23 Jul 2022 in math.FA

Abstract: In this paper, we study the so-called Bishop operators $T _ \alpha$ on $L ^ p ([0, 1])$, with $\alpha \in (0, 1)$ and $1 < p < + \infty$, from the point of view of linear dynamics. We show that they are never hypercyclic nor supercyclic, and investigate extensions of these results to the case of weighted translation operators. We then investigate the cyclicity of the Bishop operators $T _ \alpha$. Building on results by Chalendar and Partington in the case where $\alpha$ is rational, we show that $T _ \alpha$ is cyclic for a dense $G _ \delta$-set of irrational $\alpha$'s, discuss cyclic functions and provide conditions in terms of convergents of $\alpha \in \mathbf R \backslash \mathbf Q$ implying that certain functions are cyclic.

Summary

We haven't generated a summary for this paper yet.