Weak Sequentially Hypercyclic Bilateral Pseudo-Shifts Are Hypercyclic

Key Points

• The aim is to prove that weighted bilateral pseudo-shifts on certain function spaces exhibit hypercyclic behavior when weakly sequentially hypercyclic.
• Proved the result for weighted bilateral pseudo-shifts on ℓp and c0 spaces.
• Extended findings to countable direct sums of weighted pseudo-shifts.
• Established that every weighted bilateral pseudo-shift is norm hypercyclic if weakly sequentially hypercyclic.
• Generalized previous results for bilateral weighted shifts by Bès, Chan, and Sanders.