Tulane
El ala de la Fonda dedicada a la Escuela de Representación de Anillos como Secciones de Dauns y Hoffman
Alumnos
Sus alumnos fueron Takahashi, Varela y Greene.
Sus publicaciones son:
[43] A. Takahashi, Fields of Hilbert modules, Dissertation, Tulane University, New
Orleans (1971).
[44] A. Takahashi, Hilbert modules and their representations, Rev. Colombiana Mat. 13
(1979) 1–38.
[45] A. Takahashi, A duality between Hilbert modules and fields of Hilbert spaces, Rev.
Colombiana Mat. 13 (1979) 93–120.
[48] J. Varela, Duality of C∗-algebras, in [33] above, Memoirs Amer. Math. Soc. 148
(1974) 97–108.
[26] W. Greene, Ambrose Modules, in [33] below, pp. 119–142
[33] K. H. Hofmann and J. R. Liukkonen (eds.), Recent Advances in the Representation
Theory of Rings and C∗-Algebras, Memoirs Amer. Math. Soc. 148 (1974).
Resultado pRincipal
El resultado principal es el Teorema de Dauns-Hofman y la mejor referencia para su presentación es el siguiente artículo, en donde, además se dan la lista de los artículos que se publicaron en Tulane sobre la representación: [19, 22, 27–34, 43, 44, 48].
Para facilitar
[19] J. Dixmier, Ideal center of a C*-algebra, Duke Math. J. 35 (1968) 375-382.
[22] M. J. Dupré and H. M. Gillette, Banach Bundles, Banach Modules and Automorphisms of C*-Algebras, Research Notes in Math. (Pitman, London, 1983).
[27] K. H. Hofmann, Gelfand-Naimark theorems for non-commutative topological rings, in Second Symposium on General Topology and Its Relations to Modern Algebra and Analysis in Prague, 1966 (Prague, 1967 ), pp. 184-189 .
[28] K. H. Hofmann, Extending C*-algebras by adjoining an identity, in Proc. Int. Symp. on Extension Theory, Berlin, 1967 (Dt. Verl. d. Wiss., Berlin, 1969), pp. 119-125.
[29] K. H. Hofmann, Representation of rings in sheaves and fields, Bull. Amer. Math. Soc. 78(1972) 291-373 .
[30] K. H. Hofmann, Some bibliographical remarks on [30], in [33] below, pp. 177-182.
[31] K. H. Hofmann, Bundles of Banach Spaces, Sheaves of Banach Spaces, C(B)-modules, Darmstadt Lecture Notes 1974 , Mathematics Research Library (Tulane University, New Orleans, LA 70118) An H713b.
[32] \mathrm{K}. H. Hofmann, Bundles and Sheaves are equivalent in the category of Banach spaces, in K-Theory and Operutor Algebras, eds. B. Morrel and I. M. Singer, Lecture Notes in Mathematics 575(1977) 53-69.
[33] K. H. Hofmann and J. R. Liukkonen (eds.), Recent Advances in the Representation Theory of Rings and C^{4}-Algebras, Memoirs Amer. Math. Soc. 148 (1974).
[34] K. H. Hofmann and K. Keimel, Sheaf theoretical concepts in analysis: Bundles and Sheaves of Banach Spaces, Banach C(X)-modules, eds., M. P. Fourman, C. J. Mulvey and D. S. Scott, Lecture Notes in Mathematics 753(1979) 415-441.
[43] A. Takahashi, Fields of Hilbert modules, Dissertation, Tulane University, New Orleans (1971).
[44] A. Takahashi, Hilbert modules and their representations, Rev. Colombiana Mat. 13 (1979) 1-38.
[45] A. Takahashi, A duality between Hilbert modules and fields of Hilbert spaces, Rev. Colombiana Mat. 13 (1979) 93-120.
[48] J. Varela, Duality of C^{4}-algebras, in [33] above, Memoirs Amer. Math. Soc. 148 (1974) 97-108.
HOFMANN-THE DAUNS–HOFMANN THEOREM REVISITED.pdfLas publicaciones fundamentales fueron las siguientes:
[17] J. Dauns and K. H. Hofmann, Representation of rings by sections, Mem.
Amer. Math. Soc. 83 (1968) 180.
[18] J. Dauns and K. H. Hofmann, Spectral theory of algebras and adjunction of identity,
Math. Ann. 179 (1969) 175–202.
[27] K. H. Hofmann, Gelfand–Naimark theorems for non-commutative topological rings,
in Second Symposium on General Topology and Its Relations to Modern Algebra and
Analysis in Prague, 1966 (Prague, 1967), pp. 184–189.
Pero Dauns publicó sólo:
[11] J. Dauns, Representation of f-rings, Bull. Amer. Math. Soc. 74 (1968) 249–252.
[12] J. Dauns, Multiplier rings and primitive ideals, Trans. Amer. Math. Soc. 145 (1969)
125–158.
[13] J. Dauns, Representation L-groups and F-rings, Pacific J. Math. 31 (1969) 629–654.
[14] J. Dauns, The primitive ideal space of a C∗-algebra, Canadian J. Math. 26 (1974)
42–49.
[15] J. Dauns, Enveloping W∗-algebras, Rocky Mountain J. Math. 8 (1978) 589–626.
Y Hofmann sólo:
[27] K. H. Hofmann, Gelfand–Naimark theorems for non-commutative topological rings,
in Second Symposium on General Topology and Its Relations to Modern Algebra and
Analysis in Prague, 1966 (Prague, 1967), pp. 184–189.
[28] K. H. Hofmann, Extending C∗-algebras by adjoining an identity, in Proc. Int. Symp.
on Extension Theory, Berlin, 1967 (Dt. Verl. d. Wiss., Berlin, 1969), pp. 119–125.
[29] K. H. Hofmann, Representation of rings in sheaves and fields, Bull. Amer. Math. Soc.
78 (1972) 291–373.
[30] K. H. Hofmann, Some bibliographical remarks on [30], in [33] below, pp. 177–182.
[31] K. H. Hofmann, Bundles of Banach Spaces, Sheaves of Banach Spaces, C(B)-modules,
Darmstadt Lecture Notes 1974, Mathematics Research Library (Tulane University,
New Orleans, LA 70118) An H713b.
[32] K. H. Hofmann, Bundles and Sheaves are equivalent in the category of Banach spaces,
in K-Theory and Operator Algebras, eds. B. Morrel and I. M. Singer, Lecture Notes
in Mathematics 575 (1977) 53–69.
J. Algebra Appl. 2011.10:29-37. Downloaded from www.worldscientific.com
by UNIVERSITY OF HONG KONG on 09/21/13. For personal use only.
The Dauns–Hofmann Theorem Revisited 37
[33] K. H. Hofmann and J. R. Liukkonen (eds.), Recent Advances in the Representation
Theory of Rings and C∗-Algebras, Memoirs Amer. Math. Soc. 148 (1974).
[34] K. H. Hofmann and K. Keimel, Sheaf theoretical concepts in analysis: Bundles and
Sheaves of Banach Spaces, Banach C(X)-modules, eds., M. P. Fourman, C. J. Mulvey
and D. S. Scott, Lecture Notes in Mathematics 753 (1979) 415–441.
Además juntos:
[16] J. Dauns and K. H. Hofmann, The representation of biregular rings by sheaves,
Math. Z. 91 (1966) 103–123.
Seminario
En las siguientes Memorias de La AMS es la culminación del esfuerzo de Dauns y Hofmann. Su propósito de extender el Teorema de Gelfand-Naimark a anillos no conmutativos pudo haber llegado a un callejón sin salida pero como en la vida real, en matemáticas ,el sin lugar a dudas, uno de los más bellos territorios del Mundo III , lo más importante puede ser a veces el camino. El corolario del Teorema de Dauns-Hofmann que Dixmier convirtió en el TEOREMA ( leer en el pdf de arriba la simpática queja de Hofmann) es una herramienta muy útil en varios campos del análisis funcional,como muy bien lo reseña Hofmann en su sentido homenaje a su compañero de ruta con ocasión de su fallecimiento y que como homenaje a estos dos pioneros he colocado arriba.
HOFMANN-LIUKKONEN-MAMS-148-1974.pdf