Hypercyclicity in Omega

A sequence T = (Tn) of operators Tn:X → X is said to be hypercyclic if there exists a vector x ω X, called hypercyclic for T, such that {Tnx:n ≥ 0} is dense. A hypercyclic subspace for T is a closed infinitedimensional subspace of, except for zero, hypercyclic vectors. We prove that if T is a sequence of operators on. that has a hypercyclic subspace, then there exist (i) a sequence (pn) of one variable polynomials pn such that (pn). is hypercyclic for every fixed. and (ii) an operator S:→ that maps nonzero vectors onto hypercyclic vectors for T