NOTES ABOUT SUBSPACE-SUPERCYCLIC OPERATORS

A bounded linear operator T on a Banach space X is called subspace-hypercyclic for a nonzero subspace M if orb (T, x) boolean AND M is dense in M for a vector x is an element of X, where orb(T, x) = {T(n)x : n = 0, 1, 2, ...}. Similarly, the bounded linear operator T on a Banach space X is called subspace-supercyclic for a nonzero subspace M if there exists a vector whose projective orbit intersects the subspace M in a relatively dense set. In this paper we provide a Subspace-Supercyclicity Criterion and offer two equivalent conditions of this criterion. At the same time, we also characterize other properties of subspace-supercyclic operators.