Rolewicz-type chaotic operators

2015/04/09 by Donatella Bongiorno, Bongiorno, D., Udayan B. Darji +3
Mathematics · #37B99 #47A16 #47B37 #Advanced Banach Space Theory #Approximation Theory and Sequence Spaces #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.1504.02445

openalex publication_date 2015/04/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• The unconditional basic sequence problem

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