Hypercyclic shift factorizations for bilateral weighted shift operators

Abstract

Taking the perspective that a bilateral weighted shift is an operator that shifts some two-sided canonical basic sequence of ℓp(Z), with 1⩽p<∞, we show that every bilateral weighted shift on ℓp(Z) has a factorization T=AB, where A and B are hypercyclic bilateral weighted shifts. For the case when T is invertible, both shifts A and B may be selected to be invertible as well. Moreover, we show analogous hypercyclic factorization results for diagonal operators with nonzero diagonal entries.