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Abstract Let X be a compact metric space and let C ( Y ) be the space of all complex-valued continuous functions on a Hausdorff compact space Y. We prove… Click to show full abstract
Abstract Let X be a compact metric space and let C ( Y ) be the space of all complex-valued continuous functions on a Hausdorff compact space Y. We prove that the isometry group of the algebra Lip ( X , C ( Y ) ) of all C ( Y ) -valued Lipschitz maps on X, equipped with the sum norm, is topologically reflexive and 2-topologically reflexive whenever the isometry group of C ( Y ) is topologically reflexive. The same results are established for the sets of isometric reflections and generalized bi-circular projections of Lip ( X ) .
Keywords:
isometries algebras;
topologically reflexive;
valued lipschitz;
reflexivity isometries;
topological reflexivity;
lipschitz maps
Journal Title: Journal of Mathematical Analysis and Applications
Year Published: 2022
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Journal Title: Journal of Mathematical Analysis and Applications
Year Published: 2022
Link to full text (if available)
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recommendations!