Name: Li–Yorke chaotic weighted composition operators
Keywords: Fréchet sequence spaces, Linear composition operators, Frechet sequence spaces, Cyclic vectors, hypercyclic and chaotic operators, Li-Yorke chaos, weighted shifts, Dynamical Systems (math.DS), Topological dynamics, $L^p(\mu)$ spaces, C-0(X) spaces,L-p(mu) spaces

Li-Yorke chaotic weighted composition operators

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 22 Nov 2024Embargo end date: 01 Jan 2024 English Publisher:Springer Science and Business Media LLCJournal:Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, volume 119 (issn: 1578-7303, eissn: 1579-1505,

Authors: Nilson C. Bernardes; Fernanda M. Vasconcellos;

doi: 10.1007/s13398-024-01678-w , 10.48550/arxiv.2407.19091

arXiv: 2407.19091

Li–Yorke chaotic weighted composition operators

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Abstract

We establish complete characterizations of the notion of Li-Yorke chaos for weighted composition operators on $C_0(X)$ spaces and on $L^p(μ)$ spaces. As a consequence, we obtain simple characterizations of the Li-Yorke chaotic weighted shifts on $c_0$ and on $\ell^p$ ($1 \leq p < \infty$) that complement previously known results. We also investigate the notion of Li-Yorke chaos for weighted shifts on Fréchet sequence spaces. As applications, we obtain characterizations of the Li-Yorke chaotic weighted shifts on Köthe sequence spaces depending only on the entries of the Köthe matrix and the weights of the shift.

Related Organizations

Universitat Politècnica de València
Spain
Universidade Federal Fluminense
Brazil

Keywords

Fréchet sequence spaces, Linear composition operators, Frechet sequence spaces, Cyclic vectors, hypercyclic and chaotic operators, Li-Yorke chaos, weighted shifts, Dynamical Systems (math.DS), Topological dynamics, $L^p(\mu)$ spaces, C-0(X) spaces,L-p(mu) spaces, Spaces of measurable functions ($L^p$-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.), weighted composition operators, Functional Analysis (math.FA), Mathematics - Functional Analysis, Banach spaces of continuous, differentiable or analytic functions, FOS: Mathematics, Weighted composition operators, Primary 47A16, 47B33. Secondary 46E15, 46E30, 37B99, Mathematics - Dynamical Systems, Weighted shifts, $C_0(X)$ spaces

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