Weak Sequentially Hypercyclic Bilateral Pseudo-Shifts Are Hypercyclic

We prove that every weighted bilateral pseudo-shift on ℓ p ( Z ) , where 1 ≤ p < ∞ , or on c 0 ( Z ) is norm hypercyclic whenever it is weakly sequentially hypercyclic. Motivated by our result, we extend it to any countable direct sum of weighted pseudo-shifts. These results generalize those of Bès, Chan, and Sanders for the bilateral weighted shift.