On the spectrum of weighted shifts

In Linear Dynamics, the most studied class of linear operators is certainly that of weighted shifts, on the separable Banach spaces $$c_0$$ c 0 and $$\ell ^p$$ ℓ p , $$1 \le p < \infty $$ 1 ≤ p < ∞ . Over the last decades, the intensive study of such operators has produced an incredible number of versatile, deep and beautiful results that are applicable in various areas of Mathematics; and the relationships between various important notions, especially concerning chaos and hyperbolic properties, as well as spectrum of weighted shifts, have been investigated. In this paper, we investigate the point spectrum of weighted shifts and, under some regularity hypotheses on the weight sequence, we deduce the spectrum.