Masters Thesis

Linear chaos on function spaces

We show that, in the spaces Lp(0,∞) (1 ≤ p < ∞), the bounded weighted backward shift operator (Tx)(t) = wx(t + a) and its unbounded counterpart (Tx)(t) = wtx(t + a) (w > 1 and a > 0) are chaotic. We also extend the unbounded case to the space C0[0,∞) and analyze the spectral structure of the operators in both spaces provided the latter are complex.