Representation of Group Isomorphisms: The Compact Case
Let G be a discrete group and let A and B be two subgroups of G-valued continuous functions defined on two 0-dimensional compact spaces X and Y. A group isomorphism H defined between A and B is called separating when, for each pair of maps f, g∈A satisfying that f-1eG∪g-1eG=X, it holds that Hf-1eG∪H...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2015-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2015/879414 |
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| Summary: | Let G be a discrete group and let A and B be two subgroups of G-valued continuous functions defined on two 0-dimensional compact spaces X and
Y. A group isomorphism H defined between A and B is called separating when,
for each pair of maps f, g∈A satisfying that f-1eG∪g-1eG=X, it holds that
Hf-1eG∪Hg-1eG=Y. We prove that under some mild conditions every biseparating isomorphism H:A→B can be represented by means of a continuous function h:Y→X as a weighted composition operator. As a consequence we establish
the equivalence of two subgroups of continuous functions if there is a biseparating
isomorphism defined between them. |
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| ISSN: | 2314-8896 2314-8888 |