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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todo:paper_00308730_v141_n2_p279_Deferrari2023-10-03T14:40:45Z Sheaves and functional calculus Deferrari, G. Larotonda, A. Zalduendo, I. 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. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_00308730_v141_n2_p279_Deferrari |
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Universidad de Buenos Aires |
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I-28 |
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R-134 |
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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. |
| format |
JOUR |
| author |
Deferrari, G. Larotonda, A. Zalduendo, I. |
| spellingShingle |
Deferrari, G. Larotonda, A. Zalduendo, I. Sheaves and functional calculus |
| author_facet |
Deferrari, G. Larotonda, A. Zalduendo, I. |
| author_sort |
Deferrari, G. |
| 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 |
| url |
http://hdl.handle.net/20.500.12110/paper_00308730_v141_n2_p279_Deferrari |
| work_keys_str_mv |
AT deferrarig sheavesandfunctionalcalculus AT larotondaa sheavesandfunctionalcalculus AT zalduendoi sheavesandfunctionalcalculus |
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1807314529128808448 |