A NOTE ON P-SEQUENCES AND HYPERCYCLICITY

Abstract

Let 1<p <infty, a sequence {x_a}_{a \in delta} of elements of a Banach space X is called a p-sequence if there exists c> 0 such that sum_{j=1}^na_jx_{a_j}leq c|a|_p for any n in N, any a in C^n and any pairwise diffierent a_1,a_2,...,a_n in delta. A bounded operator T on a Banach space X is hypercyclic if for some vector x in X, the orbit {T^nx,n geq 0} is dense in the space. Our main result characterize p-sequence and simplify the proof of a main result in [3], which characterized hypercyclic and supercyclic bilateral weighted shifts in terms of weight sequences.