Weak Supercyclicity -- An Expository Survey
Abstract
This is an exposition on supercyclicity and weak supercyclicity, especially designed to advance further developments in weakly supercyclicity, which is a recent research field showing significant momentum during the past two decades. For operators on a normed space, the present paper explores the relationship among supercyclicity and three versions of weak supercyclicity, namely, weak l-sequential, weak sequential, and weak supercyclicities, and their connection with strong stability, weak stability, and weak quasistability. A survey of the literature on weak supercyclicity is followed by an analysis of the interplay between supercyclicity and strong stability, as well as between weak supercyclicity and weak stability. A description of the spectrum of weakly l-sequentially supercyclic operators is also given.
Keywords
Cite
@article{arxiv.2405.02752,
title = {Weak Supercyclicity -- An Expository Survey},
author = {Carlos S. Kubrusly},
journal= {arXiv preprint arXiv:2405.02752},
year = {2024}
}