Rolewicz-type chaotic operators

In this article we introduce a new class of Rolewicz-type operators in ℓpℓp, 1≤p<∞1≤p<∞. We exhibit a collection FF having the cardinality of the continuum, consisting 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.