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Deferrari, G.; Larotonda, A.; Zalduendo, I. "Sheaves and functional calculus" (1990) Pacific Journal of Mathematics. 141(2):279-286
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Abstract:

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.

Registro:

Documento: Artículo
Título:Sheaves and functional calculus
Autor:Deferrari, G.; Larotonda, A.; Zalduendo, I.
Filiación:Universidad de Buenos Aires, Pabellon I, Ciudad-Universitaria, Capital Federal Buenos Aires, 1428, Argentina
Año:1990
Volumen:141
Número:2
Página de inicio:279
Página de fin:286
DOI: http://dx.doi.org/10.2140/pjm.1990.141.279
Título revista:Pacific Journal of Mathematics
Título revista abreviado:Pac. J. Math.
ISSN:00308730
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00308730_v141_n2_p279_Deferrari

Referencias:

  • Albrecht, E., Functionalkalküle in mehreren veränderliche für stetige lineare Operatoren auf Banachraumen (1974) Manuscripta Math, 14, pp. 1-40
  • Bourbaki, N., (1967) Théories Spectrales, , Hermann, Paris
  • Bungart, L., Holomorphic functions with values in locally convex spaces and ap-plications to integral formulas (1964) Trans. Amer. Math. Soc, 3, pp. 317-344
  • Frunza, S., The Taylor spectrum and spectral decompositions (1975) J. Funct. Anal, 19, pp. 390-421
  • Gamelin, T., (1984) Uniform Algebras, , Chelsea (2nd ed.), N. Y
  • Khelemskii, A., Homological methods in Taylor holomorphic calculus of several operators in a Banach space (1981) Russ. Math. Surveys, 36 (1), pp. 139-192
  • Putinar, M., Elemente de teorie spectrala a reprezentarilor algbrelor Stein (1984) Stud. Cere. Mat, 29, pp. 193-219

Citas:

---------- APA ----------
Deferrari, G., Larotonda, A. & Zalduendo, I. (1990) . Sheaves and functional calculus. Pacific Journal of Mathematics, 141(2), 279-286.
http://dx.doi.org/10.2140/pjm.1990.141.279
---------- CHICAGO ----------
Deferrari, G., Larotonda, A., Zalduendo, I. "Sheaves and functional calculus" . Pacific Journal of Mathematics 141, no. 2 (1990) : 279-286.
http://dx.doi.org/10.2140/pjm.1990.141.279
---------- MLA ----------
Deferrari, G., Larotonda, A., Zalduendo, I. "Sheaves and functional calculus" . Pacific Journal of Mathematics, vol. 141, no. 2, 1990, pp. 279-286.
http://dx.doi.org/10.2140/pjm.1990.141.279
---------- VANCOUVER ----------
Deferrari, G., Larotonda, A., Zalduendo, I. Sheaves and functional calculus. Pac. J. Math. 1990;141(2):279-286.
http://dx.doi.org/10.2140/pjm.1990.141.279