Semi chaotic operators on Banach spaces

We introduce and study a weaker form of Devaney chaotic operators on Banach spaces, which we call semi chaotic operators. We show that semi chaotic operators exist on every finite dimensional Hilbert spaces. We give a semi chaotic criterion “a sufficient condition for semi chaotic operators”, we use this criterion to characterize all semi chaotic weighted shifts on ℓp(N) and ℓp (Z) in terms of their weight sequences