2026-06-29T08:19:32Zhttps://docta.ucm.es/rest/oai/request

oai:docta.ucm.es:20.500.14352/120062023-07-17T19:36:25Zcom_20.500.14352_14col_20.500.14352_15

The polynomial cluster value problem Prieto, Angeles Ortega, Sofia 517 517.986.225 Álgebras de Banach Álgebras uniformes Uniform algebra Strong peak point Fiber Cluster value Strong peak point Análisis matemático Análisis funcional y teoría de operadores 1202 Análisis y Análisis Funcional The 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. Ministerio de Economía y Competitividad (MINECO) Depto. de Análisis Matemático y Matemática Aplicada Fac. de Ciencias Matemáticas FALSE pub 2023-06-17T12:26:26Z 2023-06-17T12:26:26Z 2018-05-15 journal article https://hdl.handle.net/20.500.14352/12006 0022-247X 10.1016/j.jmaa.2018.01.055 eng (MTM2012-34341; MTM2015-65825-P) open access application/pdf Elsevier