Supermixing and hypermixing operators

Abstract As stronger versions of the mixing property, supermixing and hypermixing notions are introduced and investigated. We show that most of the newly known strongly hypercyclic operators satisfy the stronger condition of being hypermixing. For Banach space operators, we see that some suitable scalar multiples of any non-invertible strongly hypercyclic operator are hypermixing. We prove that on Banach spaces l p and c 0 , a weighted backward shift is supermixing if and only if it is mixing, but, a supermixing weighted backward shift is not necessarily hypermixing.