6533b874fe1ef96bd12d6210

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Rolewicz-type chaotic operators

L. Di PiazzaUdayan B. DarjiDonatella Bongiorno

subject

Pure mathematicsApplied MathematicsExistential quantificationChaoticCardinality of the continuumFunctional Analysis (math.FA)Mathematics - Functional AnalysisCorollary47A16 47B37 37B99Settore MAT/05 - Analisi MatematicaNorm (mathematics)chaotic operators hypercyclic operators lineable Rolewicz operatorFOS: MathematicsCountable setLinear combinationAnalysisMathematics

description

In this article we introduce a new class of Rolewicz-type operators in l_p, $1 \le p < \infty$. 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.

yearjournalcountryeditionlanguage
2015-01-01
http://arxiv.org/abs/1504.02445