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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Publicado: 1980
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_14467887_v29_n1_p99_Dubuc
http://hdl.handle.net/20.500.12110/paper_14467887_v29_n1_p99_Dubuc
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paper:paper_14467887_v29_n1_p99_Dubuc
record_format dspace
spelling paper:paper_14467887_v29_n1_p99_Dubuc2023-06-08T16:16:08Z 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 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. 1980 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_14467887_v29_n1_p99_Dubuc 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
collection 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.
title Uniform spaces spanier quasitopologies, and a duality for locally convex algebras
spellingShingle 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
publishDate 1980
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_14467887_v29_n1_p99_Dubuc
http://hdl.handle.net/20.500.12110/paper_14467887_v29_n1_p99_Dubuc
_version_ 1768543960905547776

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