Some Results on Subspace-Hypercyclic Operators

TL;DR

This paper investigates subspace-hypercyclic operators on Banach spaces, demonstrating their existence on all such spaces and introducing a new criterion that generalizes previous results in the field.

Contribution

It proves that every Banach space admits subspace-hypercyclic operators and establishes a novel criterion for their characterization.

Findings

Every Banach space supports subspace-hypercyclic operators.

A new criterion for identifying subspace-hypercyclic operators is provided.

Generalization of previous results by Le on subspace-hypercyclicity.

Abstract

A bounded linear operator $T$ on a Banach space $X$ is called subspace-hypercyclic if there is a subspace $M \subsetneq X$ and a vector $x \in X$ such that $orb{(x,T)} \cap M$ is dense in $M$. We show that every Banach space supports subspace-hypercyclic operators and provide a new criteira for subspace-hypercyclic operators, generalizing a previous result from Le.