Denseness of Sets of Supercyclic Vectors

TL;DR

This paper proves that various types of supercyclic vectors form dense sets in any normed space for any operator, highlighting their ubiquity regardless of the specific denseness concept used.

Contribution

It establishes the density of multiple classes of supercyclic vectors in normed spaces for arbitrary operators, regardless of the denseness notion.

Findings

All considered supercyclic vector sets are dense in the normed space.

Density holds for any notion of denseness, given the sets are nonempty.

The results apply to arbitrary operators in normed spaces.

Abstract

The sets of strongly supercyclic, weakly l-sequentially supercyclic, weakly sequentially supercyclic, and weakly supercyclic vectors for an arbitrary normed-space operator are all dense in the normed space, regardless the notion of denseness one is considering, provided they are nonempty.