On the spectrum of weighted shifts

2022/10/04 by Emma D’Aniello, Martina Maiuriello, D'Aniello, Emma +1 · 1 citation
Mathematics · #Advanced Banach Space Theory #Advanced Differential Equations and Dynamical Systems #Dynamical Systems (math.DS) #FOS: Mathematics #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.2210.01510

openalex publication_date 2022/10/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

It is well-known that, in Linear Dynamics, the most studied class of linear operators is certainly that of weighted shifts, on the separable Banach spaces c₀ and ℓ^p, 1 ≤ p< ∞. Over the last decades, the intensive study of such operators has produced an incredible number of versatile, deep and beautiful results, applicable in various areas of Mathematics and the relationships between various important notions, especially concerning chaos and hyperbolic properties, and the spectrum of weighted shifts are investigated. In this paper, we investigate the point spectrum of weighted shifts and, under some regularity hypotheses on the weight sequence, we deduce the spectrum.

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