There's something about the diameter |
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Authors: | A Aizpuru F Rambla |
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Institution: | aUniversity of Cádiz, Departamento de Matemáticas, Facultad de Ciencias, apdo. 40, 11510 Puerto Real, Cádiz, Spain |
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Abstract: | We study diameter preserving linear bijections from onto where X, Y are compact Hausdorff spaces and V, Z are Banach spaces. For instance, we obtain that if X has at least four points, Z is linearly isometric to V and either Z is a space or Z* is strictly convex or smooth, then there is a diameter preserving linear bijection from onto if and only if X is homeomorphic to Y. We also consider the case when X and Y are not compact but locally compact spaces. |
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Keywords: | Diameter Isometries Banach– Stone |
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