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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| Formato: | JOUR |
| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_14467887_v29_n1_p99_Dubuc |
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| Sumario: | 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. |
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