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arXiv · 2405.02752

Weak Supercyclicity -- An Expository Survey

Carlos S. Kubrusly
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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.

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Carlos S. Kubrusly. 2024-05-04. Weak Supercyclicity -- An Expository Survey. https://arxiv.org/abs/2405.02752

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