Generalizaciones de la dualidad de Gelfand
La dualidad de Gelfand establece una equivalencia entre la categoría de espacios compactos de Hausdorff y la categoría de C*-álgebras, que a un espacio compacto de Hausdorff X le asocia la C*-álgebra de Banach c(X,C) de funciones complejo valuadas, y a una C*-álgebra A le asocia el espacio Max(A) de...
- Autores:
-
Rodríguez Lozano, Juan Sebastián
- Tipo de recurso:
- Trabajo de grado de pregrado
- Fecha de publicación:
- 2022
- Institución:
- Universidad de los Andes
- Repositorio:
- Séneca: repositorio Uniandes
- Idioma:
- spa
- OAI Identifier:
- oai:repositorio.uniandes.edu.co:1992/64097
- Acceso en línea:
- http://hdl.handle.net/1992/64097
- Palabra clave:
- Dualidad de Gelfand
Campos topológicos
Transformada de Gelfand
Stone-Weierstrass
K-Tychonoff
Matemáticas
- Rights
- openAccess
- License
- Atribución-NoComercial 4.0 Internacional
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Generalizaciones de la dualidad de Gelfand |
| title |
Generalizaciones de la dualidad de Gelfand |
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Generalizaciones de la dualidad de Gelfand Dualidad de Gelfand Campos topológicos Transformada de Gelfand Stone-Weierstrass K-Tychonoff Matemáticas |
| title_short |
Generalizaciones de la dualidad de Gelfand |
| title_full |
Generalizaciones de la dualidad de Gelfand |
| title_fullStr |
Generalizaciones de la dualidad de Gelfand |
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Generalizaciones de la dualidad de Gelfand |
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Generalizaciones de la dualidad de Gelfand |
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Rodríguez Lozano, Juan Sebastián |
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Caicedo Ferrer, Xavier |
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Rodríguez Lozano, Juan Sebastián |
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Di Prisco, Carlos Augusto |
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Dualidad de Gelfand Campos topológicos Transformada de Gelfand Stone-Weierstrass K-Tychonoff |
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Dualidad de Gelfand Campos topológicos Transformada de Gelfand Stone-Weierstrass K-Tychonoff Matemáticas |
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Matemáticas |
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La dualidad de Gelfand establece una equivalencia entre la categoría de espacios compactos de Hausdorff y la categoría de C*-álgebras, que a un espacio compacto de Hausdorff X le asocia la C*-álgebra de Banach c(X,C) de funciones complejo valuadas, y a una C*-álgebra A le asocia el espacio Max(A) de ideales maximales con la topología de Zariski. En este trabajo exponemos la dualidad clásica y exploramos algunas posibles generalizaciones a otros campos topológicos. Probamos algunas de las generalizaciones conocidas de esta dualidad y demostramos nuevas generalizaciones en los casos que el campo K sea totalmente disconexo o cumpla con el teorema de Stone-Weierstrass. |
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V. I. Arnautov, S. T. Glavatsky, and A. V. Mikhalev. Introduction to the theory of topological rings and modules, volume 197 of Monographs and Textbooks in Pure and Applied Mathematics. Marcel Dekker, Inc., New York, 1996. G. Bachman, E. Beckenstein, L. Narici, and S. Warner. Rings of continuous functions with values in a topological field. Trans. Amer. Math. Soc., 204:91-112, 1975. V. K. Balachandran. Topological algebras, volume 185 of North-Holland Mathematics Studies. North-Holland Publishing Co., Amsterdam, 2000. Reprint of the 1999 original. X. Caicedo and G. Mantilla-Soler. On a characterization of path connected topological fields. J. Pure Appl. Algebra, 223(12):5279-5284, 2019. P. R. Chernoff, R. A. Rasala, and W. C. Waterhouse. The Stone-Weierstrass theorem for valuable fields. Pacific J. Math., 27:233-240, 1968. E. Correl and M. Henriksen. On rings of bounded continuous functions with values in a division ring. Proc. Amer. Math. Soc., 7:194-198, 1956. J. Dieudonné. Sur les corps topologiques connexes. C. R. Acad. Sci. Paris, 221:396-398, 1945. J. M. Dominguez. Non-Archimedean Gel'fand theory. Pacific J. Math., 104(2):337-341, 1983. J. Dugundji. Topology. Allyn and Bacon Series in Advanced Mathematics. Allyn and Bacon, Inc., Boston, Mass.-London-Sydney, 1978. Reprinting of the 1966 original. O. Endler. Valuation theory. Universitext. Springer-Verlag, New York-Heidelberg, 1972. To the memory of Wolfgang Krull (26 August 1899-12 April 1971). I. Gelfand. Normierte Ringe. Rec. Math. [Mat. Sbornik] N. S., 9 (51):3-24, 1941. I. Gelfand and M. Neumark. On the imbedding of normed rings into the ring of operators in Hilbert space. In C*-algebras: 1943-1993 (San Antonio, TX, 1993), volume 167 of Contemp. Math., pages 2-19. Amer. Math. Soc., Providence, RI, 1994. Corrected reprint of the 1943 original [MR 5, 147]. P. T. Johnstone. Stone spaces, volume 3 of Cambridge Studies in Advanced Mathematics. Cambridge University Press, Cambridge, 1982. R. R. Kallman and F. W. Simmons. A theorem on planar continua and an application to automorphisms of the field of complex numbers. Topology Appl., 20(3):251-255, 1985. W. Rudin. Real and complex analysis. McGraw-Hill Book Co., New York, third edition, 1987. W. Rudin. Functional analysis. International Series in Pure and Applied Mathematics. McGraw-Hill, Inc., New York, second edition, 1991. N. Shell. Connected and disconnected fields. Topology Appl., 27(1):37-50, 1987. N. Shilkret. Non-Archimedean Gelfand theory. Pacific J. Math., 32:541-550, 1970. E. M. Vechtomov. Rings and sheaves. volume 74, pages 749-798. 1995. Topology, 1. E. M. Vechtomov. Rings of continuous functions with values in a topological division ring. volume 78, pages 702-753. 1996. Topology, 2. S. Warner. Topological fields, volume 157 of North-Holland Mathematics Studies. North-Holland Publishing Co., Amsterdam, 1989. Notas de Matem´atica [Mathematical Notes], 126. A. G. Waterman and G. M. Bergman. Connected fields of arbitrary characteristic. J. Math. Kyoto Univ., 5:177-184, 1966. W. Wieslaw. Topological fields, volume 119 of Monographs and Textbooks in Pure and Applied Mathematics. Marcel Dekker, Inc., New York, 1988. S. Willard. General topology. Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, Ont., 1970. |
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Atribución-NoComercial 4.0 Internacionalhttp://creativecommons.org/licenses/by-nc/4.0/info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2Caicedo Ferrer, Xaviervirtual::6341-1Rodríguez Lozano, Juan Sebastián9f4861ec-c5a4-4e84-9595-d47fe7c066b7600Di Prisco, Carlos Augusto2023-01-23T20:37:38Z2023-01-23T20:37:38Z2022-12-09http://hdl.handle.net/1992/64097instname:Universidad de los Andesreponame:Repositorio Institucional Sénecarepourl:https://repositorio.uniandes.edu.co/La dualidad de Gelfand establece una equivalencia entre la categoría de espacios compactos de Hausdorff y la categoría de C*-álgebras, que a un espacio compacto de Hausdorff X le asocia la C*-álgebra de Banach c(X,C) de funciones complejo valuadas, y a una C*-álgebra A le asocia el espacio Max(A) de ideales maximales con la topología de Zariski. En este trabajo exponemos la dualidad clásica y exploramos algunas posibles generalizaciones a otros campos topológicos. Probamos algunas de las generalizaciones conocidas de esta dualidad y demostramos nuevas generalizaciones en los casos que el campo K sea totalmente disconexo o cumpla con el teorema de Stone-Weierstrass.MatemáticoPregrado41 páginasapplication/pdfspaUniversidad de los AndesMatemáticasFacultad de CienciasDepartamento de MatemáticasGeneralizaciones de la dualidad de GelfandTrabajo de grado - Pregradoinfo:eu-repo/semantics/bachelorThesisinfo:eu-repo/semantics/acceptedVersionhttp://purl.org/coar/resource_type/c_7a1fTexthttp://purl.org/redcol/resource_type/TPDualidad de GelfandCampos topológicosTransformada de GelfandStone-WeierstrassK-TychonoffMatemáticasV. I. Arnautov, S. T. Glavatsky, and A. V. Mikhalev. Introduction to the theory of topological rings and modules, volume 197 of Monographs and Textbooks in Pure and Applied Mathematics. Marcel Dekker, Inc., New York, 1996.G. Bachman, E. Beckenstein, L. Narici, and S. Warner. Rings of continuous functions with values in a topological field. Trans. Amer. Math. Soc., 204:91-112, 1975.V. K. Balachandran. Topological algebras, volume 185 of North-Holland Mathematics Studies. North-Holland Publishing Co., Amsterdam, 2000. Reprint of the 1999 original.X. Caicedo and G. Mantilla-Soler. On a characterization of path connected topological fields. J. Pure Appl. Algebra, 223(12):5279-5284, 2019.P. R. Chernoff, R. A. Rasala, and W. C. Waterhouse. The Stone-Weierstrass theorem for valuable fields. Pacific J. Math., 27:233-240, 1968.E. Correl and M. Henriksen. On rings of bounded continuous functions with values in a division ring. Proc. Amer. Math. Soc., 7:194-198, 1956.J. Dieudonné. Sur les corps topologiques connexes. C. R. Acad. Sci. Paris, 221:396-398, 1945.J. M. Dominguez. Non-Archimedean Gel'fand theory. Pacific J. Math., 104(2):337-341, 1983.J. Dugundji. Topology. Allyn and Bacon Series in Advanced Mathematics. Allyn and Bacon, Inc., Boston, Mass.-London-Sydney, 1978. Reprinting of the 1966 original.O. Endler. Valuation theory. Universitext. Springer-Verlag, New York-Heidelberg, 1972. To the memory of Wolfgang Krull (26 August 1899-12 April 1971).I. Gelfand. Normierte Ringe. Rec. Math. [Mat. Sbornik] N. S., 9 (51):3-24, 1941.I. Gelfand and M. Neumark. On the imbedding of normed rings into the ring of operators in Hilbert space. In C*-algebras: 1943-1993 (San Antonio, TX, 1993), volume 167 of Contemp. Math., pages 2-19. Amer. Math. Soc., Providence, RI, 1994. Corrected reprint of the 1943 original [MR 5, 147].P. T. Johnstone. Stone spaces, volume 3 of Cambridge Studies in Advanced Mathematics. Cambridge University Press, Cambridge, 1982.R. R. Kallman and F. W. Simmons. A theorem on planar continua and an application to automorphisms of the field of complex numbers. Topology Appl., 20(3):251-255, 1985.W. Rudin. Real and complex analysis. McGraw-Hill Book Co., New York, third edition, 1987.W. Rudin. Functional analysis. International Series in Pure and Applied Mathematics. McGraw-Hill, Inc., New York, second edition, 1991.N. Shell. Connected and disconnected fields. Topology Appl., 27(1):37-50, 1987.N. Shilkret. Non-Archimedean Gelfand theory. Pacific J. Math., 32:541-550, 1970.E. M. Vechtomov. Rings and sheaves. volume 74, pages 749-798. 1995. Topology, 1.E. M. Vechtomov. Rings of continuous functions with values in a topological division ring. volume 78, pages 702-753. 1996. Topology, 2.S. Warner. Topological fields, volume 157 of North-Holland Mathematics Studies. North-Holland Publishing Co., Amsterdam, 1989. Notas de Matem´atica [Mathematical Notes], 126.A. G. Waterman and G. M. Bergman. Connected fields of arbitrary characteristic. J. Math. Kyoto Univ., 5:177-184, 1966.W. Wieslaw. Topological fields, volume 119 of Monographs and Textbooks in Pure and Applied Mathematics. Marcel Dekker, Inc., New York, 1988.S. Willard. General topology. 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