Sheaves and functional calculus

Let A be a commutative Banach algebra with identity over the complex field, C. Let a1, …, an be elements of A, and sp(a) their joint spectrum. In this paper we seek to characterize the functional calculus as part of a cohomology sequence of certain sheaves, and the algebra A as the algebra of sectio...

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Autores principales: Deferrari, Graciela Inés, Larotonda, Angel Rafael, Zalduendo, Ignacio Martín
Publicado: 1990
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00308730_v141_n2_p279_Deferrari
http://hdl.handle.net/20.500.12110/paper_00308730_v141_n2_p279_Deferrari
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paper:paper_00308730_v141_n2_p279_Deferrari
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spelling paper:paper_00308730_v141_n2_p279_Deferrari2023-06-08T14:56:33Z Sheaves and functional calculus Deferrari, Graciela Inés Larotonda, Angel Rafael Zalduendo, Ignacio Martín Let A be a commutative Banach algebra with identity over the complex field, C. Let a1, …, an be elements of A, and sp(a) their joint spectrum. In this paper we seek to characterize the functional calculus as part of a cohomology sequence of certain sheaves, and the algebra A as the algebra of sections of a sheaf A, which is related to the Putinar structural sheaf. This is obtained under certain conditions on a1, …, an. The problem is related also to the unique extension property and to the local analytic spectrum σ(a, x) of x with respect to a. Section 2 is devoted to attacking this problem. In §1, some preliminary results are obtained. We also prove that if σ(a, x) is empty, then x is nilpotent. © 1990 by Pacific Journal of Mathematics. Fil:Deferrari, G. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Larotonda, A. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Zalduendo, I. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 1990 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00308730_v141_n2_p279_Deferrari http://hdl.handle.net/20.500.12110/paper_00308730_v141_n2_p279_Deferrari
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
description Let A be a commutative Banach algebra with identity over the complex field, C. Let a1, …, an be elements of A, and sp(a) their joint spectrum. In this paper we seek to characterize the functional calculus as part of a cohomology sequence of certain sheaves, and the algebra A as the algebra of sections of a sheaf A, which is related to the Putinar structural sheaf. This is obtained under certain conditions on a1, …, an. The problem is related also to the unique extension property and to the local analytic spectrum σ(a, x) of x with respect to a. Section 2 is devoted to attacking this problem. In §1, some preliminary results are obtained. We also prove that if σ(a, x) is empty, then x is nilpotent. © 1990 by Pacific Journal of Mathematics.
author Deferrari, Graciela Inés
Larotonda, Angel Rafael
Zalduendo, Ignacio Martín
spellingShingle Deferrari, Graciela Inés
Larotonda, Angel Rafael
Zalduendo, Ignacio Martín
Sheaves and functional calculus
author_facet Deferrari, Graciela Inés
Larotonda, Angel Rafael
Zalduendo, Ignacio Martín
author_sort Deferrari, Graciela Inés
title Sheaves and functional calculus
title_short Sheaves and functional calculus
title_full Sheaves and functional calculus
title_fullStr Sheaves and functional calculus
title_full_unstemmed Sheaves and functional calculus
title_sort sheaves and functional calculus
publishDate 1990
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00308730_v141_n2_p279_Deferrari
http://hdl.handle.net/20.500.12110/paper_00308730_v141_n2_p279_Deferrari
work_keys_str_mv AT deferrarigracielaines sheavesandfunctionalcalculus
AT larotondaangelrafael sheavesandfunctionalcalculus
AT zalduendoignaciomartin sheavesandfunctionalcalculus
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