Uniformly continuous functions on non-Hausdorff groupoids
The purpose of this paper is to study the notion of uniform continuity introduced in [M. Buneci, Haar systems and homomorphism on groupoids, Operator algebras and mathematical physics, 35-49, Theta, Bucharest, 2003]. For a locally compact (not necessarily Hausdorff) groupoid endowed with pre-Haar...
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| Format: | Article |
| Language: | English |
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University Constantin Brancusi of Targu-Jiu
2010-09-01
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| Series: | Surveys in Mathematics and its Applications |
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| Online Access: | http://www.utgjiu.ro/math/sma/v05/p17.pdf |
| Summary: | The purpose of this paper is to study the notion of uniform continuity introduced in [M. Buneci, Haar systems and homomorphism on groupoids, Operator algebras and mathematical physics, 35-49, Theta, Bucharest, 2003]. For a locally compact (not necessarily Hausdorff) groupoid endowed with pre-Haar systems, we prove that the space of bounded compactly supported functions which are left and right uniformly continuous on fibres can be made into a *-algebra and endowed with a (reduced) C<SUP>*</SUP>-norm. The advantage of working with uniformly continuous on fibres functions is the fact that even if the groupoid does not admit a continuous Haar system, various C<SUP>*</SUP>-algebras can be associated with it. |
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| ISSN: | 1843-7265 1842-6298 |