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Representation of Group Isomorphisms: The Compact Case
dc.contributor.author | Ferrer González, María Vicenta | |
dc.contributor.author | Gary Gutierrez, Margarita | |
dc.contributor.author | Hernández, Salvador | |
dc.date.accessioned | 2016-06-14T10:27:17Z | |
dc.date.available | 2016-06-14T10:27:17Z | |
dc.date.issued | 2015 | |
dc.identifier.citation | Ferrer, M., Gary, M., & Hernández, S. (2015). Representation of Group Isomorphisms: The Compact Case. Journal of Function Spaces, 2015. | ca_CA |
dc.identifier.uri | http://hdl.handle.net/10234/160680 | |
dc.description.abstract | 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�−1(𝑒� 𝐺� ) ∪ 𝑔�−1(𝑒� 𝐺� ) = 𝑋�, it holds that 𝐻�𝑓�−1(𝑒� 𝐺� ) ∪ 𝐻�𝑔�−1(𝑒� 𝐺� ) = 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. | ca_CA |
dc.description.sponsorShip | The authors thank the referee for several valuable comments. The first and third listed authors acknowledge the partial support provided by the Generalitat Valenciana, Grant code: PROMETEO/2014/062, and by Universitat Jaume I, Grant P1.1B2012-05. | ca_CA |
dc.format.extent | 6 p. | ca_CA |
dc.format.mimetype | application/pdf | ca_CA |
dc.language.iso | eng | ca_CA |
dc.publisher | Hindawi Publishing Corporation | ca_CA |
dc.relation.isPartOf | Journal of Function Spaces Volume 2015 (2015), Article ID 879414, | ca_CA |
dc.rights | Copyright © 2015 Marita Ferrer et al. | ca_CA |
dc.rights | Attribution 4.0 Spain | * |
dc.rights.uri | http://creativecommons.org/licenses/by-sa/4.0/ | * |
dc.subject | group isomorphism | ca_CA |
dc.title | Representation of Group Isomorphisms: The Compact Case | ca_CA |
dc.type | info:eu-repo/semantics/article | ca_CA |
dc.identifier.doi | http://dx.doi.org/10.1155/2015/879414 | |
dc.rights.accessRights | info:eu-repo/semantics/openAccess | ca_CA |
dc.relation.publisherVersion | http://www.hindawi.com/journals/jfs/2015/879414/abs/ | ca_CA |
dc.type.version | info:eu-repo/semantics/publishedVersion |
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