Some Results on Subspace-Hypercyclic Operators

Abstract

A bounded linear operator $T$ on a Banach space $X$ is called subspace-hypercyclic if there is a subspace $M⊊X$ 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.