Representation of Group Isomorphisms: The Compact Case. (3rd February 2015)

• Record Type: Journal Article
• Authors: Ferrer, Marita; Gary, Margarita; Hernández, Salvador
• Other Names: Leiva Hugo Academic Editor.
• Is Part Of: Journal of function spaces. Volume 2015(2015)
• Publication Date: 2015-02-03
• Subjects: Function spaces -- Periodicals; 515.7305
• DOI: 10.1155/2015/879414
• Languages: English
• ISSNs: 2314-8896

Abstract

Abstract : LetG be a discrete group and letA andB be two subgroups ofG -valued continuous functions defined on two 0-dimensional compact spacesX andY . A group isomorphismH defined betweenA andB is called separating when, for each pair of mapsf, g ∈ A satisfying thatf - 1 e G ∪ g - 1 e G = X, it holds thatH f - 1 e G ∪ H g - 1 e G = Y . We prove that under some mild conditions every biseparating isomorphismH : A → B can be represented by means of a continuous functionh : 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.