Seco Forsnacke, DanielTéllez, Roberto2021-05-142022-01-012021-01Seco, D. & Téllez, R. (2021). Polynomial approach to cyclicity for weighted ℓpA. Banach Journal of Mathematical Analysis, 15(1), 1.1735-8787https://hdl.handle.net/10016/32638In previous works, an approach to the study of cyclic functions in reproducing kernel Hilbert spaces has been presented, based on the study of so called optimal polynomial approximants. In the present article, we extend such approach to the (non-Hilbert) case of spaces of analytic functions whose Taylor coefficients are in ℓp(ω), for some weight ω. When ω={(k+1)α}k∈N, for a fixed α∈R, we derive a characterization of the cyclicity of polynomial functions and, when 1 < p < ∞, we obtain sharp rates of convergence of the optimal norms.16eng© 2020, Tusi Mathematical Research Group (TMRG)Analytic function spacesCyclic functionsOptimal polynomial approximantsresearch articleMatemáticashttps://doi.org/10.1007/s43037-020-00085-8open access1116Banach Journal of Mathematical Analysis15AR/0000027606