Prieto, AngelesOrtega, Sofia2023-06-172023-06-172018-05-150022-247X10.1016/j.jmaa.2018.01.055https://hdl.handle.net/20.500.14352/12006The polynomial cluster value problem replaces the role of the continuous linear functionals in the original cluster value problem for the continuous polynomials to describe the corresponding cluster sets and fibers. We prove several polynomial cluster value theorems for uniform algebras H(B) between A(u)(B) and H-infinity (B), where B is the open unit ball of a complex Banach space X. We also obtain new results about the original cluster value problem, especially for A(infinity) (B). Examples of spaces X considered here are spaces of continuous functions, l(1) and locally uniformly convex spaces. (C) 2018 Elsevier Inc. All rights reserved.engThe polynomial cluster value problemjournal articlehttps://doi.org/10.1016/j.jmaa.2018.01.055https://www.elsevier.com/open access517517.986.225Álgebras de BanachÁlgebras uniformesUniform algebra Strong peak pointFiberCluster valueStrong peak pointAnálisis matemáticoAnálisis funcional y teoría de operadores1202 Análisis y Análisis Funcional