  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.
