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Algebraic reflexivity of the isometry group of some spaces of Lipschitz functions. (English) Zbl 1194.46012

Summary: We show that the isometry groups of Lip\((X,d)\) and lip\((X,d^\alpha )\) with \(\alpha \in (0,1)\), for a compact metric space (\(X,d\)), are algebraically reflexive. We also prove that the sets of isometric reflections and generalized bi-circular projections on such spaces are algebraically reflexive. In order to achieve this, we characterize generalized bi-circular projections on these spaces.

MSC:

46B04 Isometric theory of Banach spaces
46E15 Banach spaces of continuous, differentiable or analytic functions
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