Holomorphic functions and polynomial ideals on Banach spaces

Given a multiplicative sequence of polynomial ideals, we consider the associated algebra of holomorphic functions of bounded type. We prove that, under very natural conditions satisfied by many usual classes of polynomials, the spectrum of this algebra "behaves" like the classical case of...

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Detalles Bibliográficos
Autores principales: Carando, Daniel German, Dimant, Verónica, Muro, Santiago
Publicado: 2012
Materias:
Holomorphic functions
Polynomial ideals
Riemann domains over banach spaces
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00100757_v63_n1_p71_Carando
http://hdl.handle.net/20.500.12110/paper_00100757_v63_n1_p71_Carando
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paper:paper_00100757_v63_n1_p71_Carando
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spelling paper:paper_00100757_v63_n1_p71_Carando2023-06-08T14:34:16Z Holomorphic functions and polynomial ideals on Banach spaces Carando, Daniel German Dimant, Verónica Muro, Santiago Holomorphic functions Polynomial ideals Riemann domains over banach spaces Given a multiplicative sequence of polynomial ideals, we consider the associated algebra of holomorphic functions of bounded type. We prove that, under very natural conditions satisfied by many usual classes of polynomials, the spectrum of this algebra "behaves" like the classical case of M b(E) (the spectrum of H b(E), the algebra of bounded type holomorphic functions). More precisely, we prove that can be endowed with a structure of Riemann domain over E′′ and that the extension of each -holomorphic function of bounded type in each connected component. We also prove a Banach-Stone type theorem for these algebras. © 2010 Universitat de Barcelona. Fil:Carando, D. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Dimant, V. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Muro, S. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2012 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00100757_v63_n1_p71_Carando http://hdl.handle.net/20.500.12110/paper_00100757_v63_n1_p71_Carando
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Holomorphic functions
Polynomial ideals
Riemann domains over banach spaces
spellingShingle Holomorphic functions
Polynomial ideals
Riemann domains over banach spaces
Carando, Daniel German
Dimant, Verónica
Muro, Santiago
Holomorphic functions and polynomial ideals on Banach spaces
topic_facet Holomorphic functions
Polynomial ideals
Riemann domains over banach spaces
description Given a multiplicative sequence of polynomial ideals, we consider the associated algebra of holomorphic functions of bounded type. We prove that, under very natural conditions satisfied by many usual classes of polynomials, the spectrum of this algebra "behaves" like the classical case of M b(E) (the spectrum of H b(E), the algebra of bounded type holomorphic functions). More precisely, we prove that can be endowed with a structure of Riemann domain over E′′ and that the extension of each -holomorphic function of bounded type in each connected component. We also prove a Banach-Stone type theorem for these algebras. © 2010 Universitat de Barcelona.
author Carando, Daniel German
Dimant, Verónica
Muro, Santiago
author_facet Carando, Daniel German
Dimant, Verónica
Muro, Santiago
author_sort Carando, Daniel German
title Holomorphic functions and polynomial ideals on Banach spaces
title_short Holomorphic functions and polynomial ideals on Banach spaces
title_full Holomorphic functions and polynomial ideals on Banach spaces
title_fullStr Holomorphic functions and polynomial ideals on Banach spaces
title_full_unstemmed Holomorphic functions and polynomial ideals on Banach spaces
title_sort holomorphic functions and polynomial ideals on banach spaces
publishDate 2012
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00100757_v63_n1_p71_Carando
http://hdl.handle.net/20.500.12110/paper_00100757_v63_n1_p71_Carando
work_keys_str_mv AT carandodanielgerman holomorphicfunctionsandpolynomialidealsonbanachspaces
AT dimantveronica holomorphicfunctionsandpolynomialidealsonbanachspaces
AT murosantiago holomorphicfunctionsandpolynomialidealsonbanachspaces
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