Rolewicz-type chaotic operators

Abstract

In this article we introduce a new class of Rolewicz-type operators in ℓ p , 1 ≤ p < ∞. We exhibit a collection F of cardinality continuum of operators of this type which are chaotic and remain so under almost all finite linear combinations, provided that the linear combination has sufficiently large norm. As a corollary to our main result we also obtain that there exists a countable collection of such operators whose all finite linear combinations are chaotic provided that they have sufficiently large norm.