Uniform spaces spanier quasitopologies, and a duality for locally convex algebras
Gelfand-type duality results can be obtained for locally convex algebras using a quasitopological structure on the spectrum of an algebra (as opposed to the topologies traditionally considered). In this way, the duality between (commutative, with identity) C*-algebras and compact spaces can be exten...
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todo:paper_14467887_v29_n1_p99_Dubuc2023-10-03T16:16:28Z Uniform spaces spanier quasitopologies, and a duality for locally convex algebras Dubuc, E.J. Gelfand-type duality results can be obtained for locally convex algebras using a quasitopological structure on the spectrum of an algebra (as opposed to the topologies traditionally considered). In this way, the duality between (commutative, with identity) C*-algebras and compact spaces can be extended to pro-C*-algebras and separated quasitopologies. The extension is provided by a functional representation of an algebra A as the algebra of all continuous numerical functions on a quasitopological space. The first half of the paper deals with uniform spaces and quasitopologies, and has independent interest. © 1980, Australian Mathematical Society. All rights reserved. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_14467887_v29_n1_p99_Dubuc |
| institution |
Universidad de Buenos Aires |
| institution_str |
I-28 |
| repository_str |
R-134 |
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
| description |
Gelfand-type duality results can be obtained for locally convex algebras using a quasitopological structure on the spectrum of an algebra (as opposed to the topologies traditionally considered). In this way, the duality between (commutative, with identity) C*-algebras and compact spaces can be extended to pro-C*-algebras and separated quasitopologies. The extension is provided by a functional representation of an algebra A as the algebra of all continuous numerical functions on a quasitopological space. The first half of the paper deals with uniform spaces and quasitopologies, and has independent interest. © 1980, Australian Mathematical Society. All rights reserved. |
| format |
JOUR |
| author |
Dubuc, E.J. |
| spellingShingle |
Dubuc, E.J. Uniform spaces spanier quasitopologies, and a duality for locally convex algebras |
| author_facet |
Dubuc, E.J. |
| author_sort |
Dubuc, E.J. |
| title |
Uniform spaces spanier quasitopologies, and a duality for locally convex algebras |
| title_short |
Uniform spaces spanier quasitopologies, and a duality for locally convex algebras |
| title_full |
Uniform spaces spanier quasitopologies, and a duality for locally convex algebras |
| title_fullStr |
Uniform spaces spanier quasitopologies, and a duality for locally convex algebras |
| title_full_unstemmed |
Uniform spaces spanier quasitopologies, and a duality for locally convex algebras |
| title_sort |
uniform spaces spanier quasitopologies, and a duality for locally convex algebras |
| url |
http://hdl.handle.net/20.500.12110/paper_14467887_v29_n1_p99_Dubuc |
| work_keys_str_mv |
AT dubucej uniformspacesspanierquasitopologiesandadualityforlocallyconvexalgebras |
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1807319735879073792 |